diff --git a/libcxx/docs/Status/RangesAlgorithms.csv b/libcxx/docs/Status/RangesAlgorithms.csv
--- a/libcxx/docs/Status/RangesAlgorithms.csv
+++ b/libcxx/docs/Status/RangesAlgorithms.csv
@@ -82,8 +82,8 @@
 Permutation,push_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
 Permutation,pop_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
 Permutation,sort_heap,Konstantin Varlamov,`D128115 <https://llvm.org/D128115>`_,✅
-Permutation,prev_permutation,Not assigned,n/a,Not started
-Permutation,next_permutation,Not assigned,n/a,Not started
+Permutation,Nikolas Klauser,`D129859 <https://llvm.org/D129859>`_,✅
+Permutation,Nikolas Klauser,`D129859 <https://llvm.org/D129859>`_,✅
 Uninitialised memory,uninitialized_copy,Konstantin Varlamov,`D116023 <https://llvm.org/D116023>`_,✅
 Uninitialised memory,uninitialized_copy_n,Konstantin Varlamov,`D116023 <https://llvm.org/D116023>`_,✅
 Uninitialised memory,uninitialized_fill,Konstantin Varlamov,`D115626 <https://llvm.org/D115626>`_,✅
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -111,6 +111,7 @@
   __algorithm/ranges_mismatch.h
   __algorithm/ranges_move.h
   __algorithm/ranges_move_backward.h
+  __algorithm/ranges_next_permutation.h
   __algorithm/ranges_none_of.h
   __algorithm/ranges_nth_element.h
   __algorithm/ranges_partial_sort_copy.h
@@ -119,6 +120,7 @@
   __algorithm/ranges_partition_point.h
   __algorithm/ranges_pop_heap.h
   __algorithm/ranges_push_heap.h
+  __algorithm/ranges_prev_permutation.h
   __algorithm/ranges_remove.h
   __algorithm/ranges_remove_copy.h
   __algorithm/ranges_remove_copy_if.h
diff --git a/libcxx/include/__algorithm/ranges_next_permutation.h b/libcxx/include/__algorithm/ranges_next_permutation.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_next_permutation.h
@@ -0,0 +1,60 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_NEXT_PERMUTATION_H
+#define _LIBCPP___ALGORITHM_RANGES_NEXT_PERMUTATION_H
+
+#include <__algorithm/in_found_result.h>
+#include <__algorithm/ranges_prev_permutation.h>
+#include <__config>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+namespace ranges {
+
+template <class _InIter>
+using next_permutation_result = in_found_result<_InIter>;
+
+namespace __next_permutation {
+
+struct __fn {
+  template <bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr next_permutation_result<_Iter>
+  operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    auto __comp_reverse_args = [&](auto&& __lhs, auto&& __rhs) { return std::invoke(__comp, __rhs, __lhs); };
+    return ranges::__prev_permutation_impl(__first, __last, __comp_reverse_args, __proj);
+  }
+
+  template <bidirectional_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr next_permutation_result<borrowed_iterator_t<_Range>>
+  operator()(_Range&& __range, _Comp __comp = {}, _Proj __proj = {}) const {
+    auto __comp_reverse_args = [&](auto&& __lhs, auto&& __rhs) { return std::invoke(__comp, __rhs, __lhs); };
+    return ranges::__prev_permutation_impl(ranges::begin(__range), ranges::end(__range), __comp_reverse_args, __proj);
+  }
+};
+
+} // namespace __next_permutation
+
+inline namespace __cpo {
+constexpr inline auto next_permutation = __next_permutation::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP___ALGORITHM_RANGES_NEXT_PERMUTATION_H
diff --git a/libcxx/include/__algorithm/ranges_prev_permutation.h b/libcxx/include/__algorithm/ranges_prev_permutation.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_prev_permutation.h
@@ -0,0 +1,92 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef _LIBCPP___ALGORITHM_RANGES_PREV_PERMUTATION_H
+#define _LIBCPP___ALGORITHM_RANGES_PREV_PERMUTATION_H
+
+#include <__algorithm/in_found_result.h>
+#include <__algorithm/ranges_reverse.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iter_swap.h>
+#include <__iterator/next.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+namespace ranges {
+
+template <class _InIter>
+using prev_permutation_result = in_found_result<_InIter>;
+
+template <class _Iter, class _Sent, class _Comp, class _Proj>
+_LIBCPP_HIDE_FROM_ABI constexpr prev_permutation_result<_Iter>
+__prev_permutation_impl(_Iter __first, _Sent __sent, _Comp& __comp, _Proj& __proj) {
+  auto __last = ranges::next(__first, __sent);
+  auto __i = __last;
+  if (__first == __last || __first == --__i)
+    return {std::move(__last), false};
+  while (true) {
+    auto __ip1 = __i;
+    --__i;
+    if (std::invoke(__comp, std::invoke(__proj, *__ip1), std::invoke(__proj, *__i))) {
+      auto __j = __last;
+      do {
+        --__j;
+      } while (!std::invoke(__comp, std::invoke(__proj, *__j), std::invoke(__proj, *__i)));
+      ranges::iter_swap(__i, __j);
+      ranges::reverse(__ip1, __last);
+      return {std::move(__last), true};
+    }
+    if (__i == __first) {
+      ranges::reverse(__first, __last);
+      return {std::move(__last), false};
+    }
+  }
+}
+
+namespace __prev_permutation {
+
+struct __fn {
+  template <bidirectional_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr prev_permutation_result<_Iter>
+  operator()(_Iter __first, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return ranges::__prev_permutation_impl(__first, __last, __comp, __proj);
+  }
+
+  template <bidirectional_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr prev_permutation_result<borrowed_iterator_t<_Range>>
+  operator()(_Range&& __range, _Comp __comp = {}, _Proj __proj = {}) const {
+    return ranges::__prev_permutation_impl(ranges::begin(__range), ranges::end(__range), __comp, __proj);
+  }
+};
+} // namespace __prev_permutation
+
+inline namespace __cpo {
+constexpr inline auto prev_permutation = __prev_permutation::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP___ALGORITHM_RANGES_PREV_PERMUTATION_H
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -703,7 +703,7 @@
       set_symmetric_difference(I1 first1, S1 last1, I2 first2, S2 last2, O result,
                                Comp comp = {}, Proj1 proj1 = {},
                                Proj2 proj2 = {});                                                   // since C++20
-  
+
   template<input_range R1, input_range R2, weakly_incrementable O,
            class Comp = ranges::less, class Proj1 = identity, class Proj2 = identity>
     requires mergeable<iterator_t<R1>, iterator_t<R2>, O, Comp, Proj1, Proj2>
@@ -711,7 +711,7 @@
                                                       borrowed_iterator_t<R2>, O>
       set_symmetric_difference(R1&& r1, R2&& r2, O result, Comp comp = {},
                                Proj1 proj1 = {}, Proj2 proj2 = {});                                 // since C++20
-  
+
   template<class I1, class I2, class O>
     using set_union_result = in_in_out_result<I1, I2, O>;                                           // since C++20
 
@@ -729,6 +729,31 @@
     constexpr set_union_result<borrowed_iterator_t<R1>, borrowed_iterator_t<R2>, O>
       set_union(R1&& r1, R2&& r2, O result, Comp comp = {},
                 Proj1 proj1 = {}, Proj2 proj2 = {});                                                // since C++20
+
+  template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+           class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr ranges::prev_permutation_result<I>
+      ranges::prev_permutation(I first, S last, Comp comp = {}, Proj proj = {});                    // since C++20
+
+  template<bidirectional_range R, class Comp = ranges::less,
+           class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr ranges::prev_permutation_result<borrowed_iterator_t<R>>
+      ranges::prev_permutation(R&& r, Comp comp = {}, Proj proj = {});                              // since C++20
+
+  template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+           class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr ranges::next_permutation_result<I>
+      ranges::next_permutation(I first, S last, Comp comp = {}, Proj proj = {});                    // since C++20
+
+  template<bidirectional_range R, class Comp = ranges::less,
+           class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr ranges::next_permutation_result<borrowed_iterator_t<R>>
+      ranges::next_permutation(R&& r, Comp comp = {}, Proj proj = {});                              // since C++20
+
 }
 
     constexpr bool     // constexpr in C++20
@@ -1494,9 +1519,11 @@
 #include <__algorithm/ranges_mismatch.h>
 #include <__algorithm/ranges_move.h>
 #include <__algorithm/ranges_move_backward.h>
+#include <__algorithm/ranges_next_permutation.h>
 #include <__algorithm/ranges_none_of.h>
 #include <__algorithm/ranges_nth_element.h>
 #include <__algorithm/ranges_pop_heap.h>
+#include <__algorithm/ranges_prev_permutation.h>
 #include <__algorithm/ranges_push_heap.h>
 #include <__algorithm/ranges_remove.h>
 #include <__algorithm/ranges_remove_if.h>
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_comparators.pass.cpp
@@ -165,8 +165,8 @@
     (void)std::ranges::minmax_element(a, Less(&copies)); assert(copies == 0);
     (void)std::ranges::mismatch(first, last, first2, last2, Equal(&copies)); assert(copies == 0);
     (void)std::ranges::mismatch(a, b, Equal(&copies)); assert(copies == 0);
-    //(void)std::ranges::next_permutation(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::next_permutation(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::next_permutation(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::next_permutation(a, Less(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(first, last, UnaryTrue(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(a, UnaryTrue(&copies)); assert(copies == 0);
     (void)std::ranges::nth_element(first, mid, last, Less(&copies)); assert(copies == 0);
@@ -183,8 +183,8 @@
     //(void)std::ranges::partition_point(a, UnaryTrue(&copies)); assert(copies == 0);
     (void)std::ranges::pop_heap(first, last, Less(&copies)); assert(copies == 0);
     (void)std::ranges::pop_heap(a, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::prev_permutation(first, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::prev_permutation(a, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::prev_permutation(first, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::prev_permutation(a, Less(&copies)); assert(copies == 0);
     (void)std::ranges::push_heap(first, last, Less(&copies)); assert(copies == 0);
     (void)std::ranges::push_heap(a, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy_if(first, last, first2, UnaryTrue(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
--- a/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
+++ b/libcxx/test/libcxx/algorithms/ranges_robust_against_copying_projections.pass.cpp
@@ -148,8 +148,8 @@
     (void)std::ranges::minmax_element(a, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::mismatch(first, last, first2, last2, Equal(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::mismatch(a, b, Equal(), Proj(&copies), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::next_permutation(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::next_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::next_permutation(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::next_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(first, last, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::none_of(a, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::nth_element(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
@@ -166,8 +166,8 @@
     //(void)std::ranges::partition_point(a, UnaryTrue(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::pop_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::pop_heap(a, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::prev_permutation(first, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::prev_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::prev_permutation(first, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::prev_permutation(a, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::push_heap(first, last, Less(), Proj(&copies)); assert(copies == 0);
     (void)std::ranges::push_heap(a, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::remove_copy(first, last, first2, value, Proj(&copies)); assert(copies == 0);
diff --git a/libcxx/test/libcxx/private_headers.verify.cpp b/libcxx/test/libcxx/private_headers.verify.cpp
--- a/libcxx/test/libcxx/private_headers.verify.cpp
+++ b/libcxx/test/libcxx/private_headers.verify.cpp
@@ -148,6 +148,7 @@
 #include <__algorithm/ranges_mismatch.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_mismatch.h'}}
 #include <__algorithm/ranges_move.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_move.h'}}
 #include <__algorithm/ranges_move_backward.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_move_backward.h'}}
+#include <__algorithm/ranges_next_permutation.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_next_permutation.h'}}
 #include <__algorithm/ranges_none_of.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_none_of.h'}}
 #include <__algorithm/ranges_nth_element.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_nth_element.h'}}
 #include <__algorithm/ranges_partial_sort_copy.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_partial_sort_copy.h'}}
@@ -155,6 +156,7 @@
 #include <__algorithm/ranges_partition_copy.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_partition_copy.h'}}
 #include <__algorithm/ranges_partition_point.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_partition_point.h'}}
 #include <__algorithm/ranges_pop_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_pop_heap.h'}}
+#include <__algorithm/ranges_prev_permutation.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_prev_permutation.h'}}
 #include <__algorithm/ranges_push_heap.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_push_heap.h'}}
 #include <__algorithm/ranges_remove.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_remove.h'}}
 #include <__algorithm/ranges_remove_copy.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_remove_copy.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.next_permutation.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.next_permutation.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.next_permutation.pass.cpp
@@ -0,0 +1,140 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//          class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr ranges::next_permutation_result<I>
+//     ranges::next_permutation(I first, S last, Comp comp = {}, Proj proj = {});
+// template<bidirectional_range R, class Comp = ranges::less,
+//          class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr ranges::next_permutation_result<borrowed_iterator_t<R>>
+//     ranges::next_permutation(R&& r, Comp comp = {}, Proj proj = {});
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstddef>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "test_iterators.h"
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>>
+concept HasNextPermutationIt = requires(Iter first, Sent last) { std::ranges::next_permutation(first, last); };
+
+static_assert(HasNextPermutationIt<int*>);
+static_assert(!HasNextPermutationIt<BidirectionalIteratorNotDerivedFrom>);
+static_assert(!HasNextPermutationIt<BidirectionalIteratorNotDecrementable>);
+static_assert(!HasNextPermutationIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasNextPermutationIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasNextPermutationIt<const int*>); // not sortable
+
+template <class Range>
+concept HasNextPermutationR = requires(Range range) { std::ranges::next_permutation(range); };
+
+static_assert(HasNextPermutationR<UncheckedRange<int*>>);
+static_assert(!HasNextPermutationR<BidirectionalRangeNotDerivedFrom>);
+static_assert(!HasNextPermutationR<BidirectionalRangeNotDecrementable>);
+static_assert(!HasNextPermutationR<BidirectionalRangeNotSentinelSemiregular>);
+static_assert(!HasNextPermutationR<BidirectionalRangeNotSentinelWeaklyEqualityComparableWith>);
+static_assert(!HasNextPermutationR<UncheckedRange<const int*>>); // not sortable
+
+constexpr size_t factorial(size_t i) {
+  size_t result = 1;
+  for (; i != 0; --i)
+    result *= i;
+  return result;
+}
+
+template <class Iter, class Sent>
+void test_permutations() {
+  auto test_prev_permutations = [](auto call_prev_permutation) {
+    auto input = std::array{1, 2, 3, 4, 5, 6};
+    std::array<int, input.size()> last_permutation;
+    for (size_t i = 0; i <= input.size(); ++i) {
+      size_t count = 0;
+
+      bool found_permutation = true;
+      while (found_permutation) {
+        last_permutation = input;
+        std::same_as<std::ranges::prev_permutation_result<Iter>> decltype(auto) ret =
+            call_prev_permutation(Iter(input.data()), Sent(Iter(input.data() + i)));
+        found_permutation = ret.found;
+        assert(base(ret.in) == input.data() + i);
+        if (i > 1) {
+          auto input_subrange            = input | std::views::take(i);
+          auto last_permutation_subrange = last_permutation | std::views::take(i);
+          if (found_permutation)
+            assert(std::ranges::lexicographical_compare(last_permutation_subrange, input_subrange));
+          else
+            assert(std::ranges::lexicographical_compare(input_subrange, last_permutation_subrange));
+        }
+        ++count;
+      }
+      assert(count == factorial(i));
+    }
+    return true;
+  };
+
+  auto iterator_overload = [](auto&& first, auto&& last) { return std::ranges::next_permutation(first, last); };
+  auto range_overload    = [](auto&& first, auto&& last) {
+    auto range = std::ranges::subrange(first, last);
+    return std::ranges::next_permutation(range);
+  };
+
+  if constexpr (std::is_same_v<Iter, Sent>) {
+    auto iterator_overload_counted =
+        [](auto first, auto last) -> std::ranges::prev_permutation_result<decltype(first)> {
+      int count = 0;
+      auto ret = std::ranges::next_permutation(SwapCountingIterator(first, &count), SwapCountingIterator(last, &count));
+      assert(count <= (base(last) - base(first) + 1) / 2);
+      return ret;
+    };
+
+    auto range_overload_counted = [](auto first, auto last) -> std::ranges::prev_permutation_result<decltype(first)> {
+      int count  = 0;
+      auto range = std::ranges::subrange(SwapCountingIterator(first, &count), SwapCountingIterator(last, &count));
+      auto ret   = std::ranges::next_permutation(range);
+      assert(count <= (base(last) - base(first) + 1) / 2);
+      return ret;
+    };
+
+    test_prev_permutations(iterator_overload_counted);
+    static_assert(test_prev_permutations(iterator_overload_counted));
+    test_prev_permutations(range_overload_counted);
+    static_assert(test_prev_permutations(range_overload_counted));
+  }
+
+  test_prev_permutations(iterator_overload);
+  static_assert(test_prev_permutations(iterator_overload));
+  test_prev_permutations(range_overload);
+  static_assert(test_prev_permutations(range_overload));
+}
+
+template <class Iter>
+void test_sentinels() {
+  test_permutations<Iter, Iter>();
+  test_permutations<Iter, sentinel_wrapper<Iter>>();
+  test_permutations<Iter, sized_sentinel<Iter>>();
+}
+
+void test() {
+  test_sentinels<bidirectional_iterator<int*>>();
+  test_sentinels<random_access_iterator<int*>>();
+  test_sentinels<contiguous_iterator<int*>>();
+  test_sentinels<int*>();
+}
+
+int main(int, char**) { test(); }
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.prev_permutation.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.prev_permutation.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.permutation.generators/ranges.prev_permutation.pass.cpp
@@ -0,0 +1,140 @@
+//===----------------------------------------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+// <algorithm>
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// template<bidirectional_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//          class Proj = identity>
+//   requires sortable<I, Comp, Proj>
+//   constexpr ranges::prev_permutation_result<I>
+//     ranges::prev_permutation(I first, S last, Comp comp = {}, Proj proj = {});
+// template<bidirectional_range R, class Comp = ranges::less,
+//          class Proj = identity>
+//   requires sortable<iterator_t<R>, Comp, Proj>
+//   constexpr ranges::prev_permutation_result<borrowed_iterator_t<R>>
+//     ranges::prev_permutation(R&& r, Comp comp = {}, Proj proj = {});
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <cstddef>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "test_iterators.h"
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>>
+concept HasPrevPermutationIt = requires(Iter first, Sent last) { std::ranges::prev_permutation(first, last); };
+
+static_assert(HasPrevPermutationIt<int*>);
+static_assert(!HasPrevPermutationIt<BidirectionalIteratorNotDerivedFrom>);
+static_assert(!HasPrevPermutationIt<BidirectionalIteratorNotDecrementable>);
+static_assert(!HasPrevPermutationIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasPrevPermutationIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasPrevPermutationIt<const int*>); // not sortable
+
+template <class Range>
+concept HasPrevPermutationR = requires(Range range) { std::ranges::prev_permutation(range); };
+
+static_assert(HasPrevPermutationR<UncheckedRange<int*>>);
+static_assert(!HasPrevPermutationR<BidirectionalRangeNotDerivedFrom>);
+static_assert(!HasPrevPermutationR<BidirectionalRangeNotDecrementable>);
+static_assert(!HasPrevPermutationR<BidirectionalRangeNotSentinelSemiregular>);
+static_assert(!HasPrevPermutationR<BidirectionalRangeNotSentinelWeaklyEqualityComparableWith>);
+static_assert(!HasPrevPermutationR<UncheckedRange<const int*>>); // not sortable
+
+constexpr size_t factorial(size_t i) {
+  size_t result = 1;
+  for (; i != 0; --i)
+    result *= i;
+  return result;
+}
+
+template <class Iter, class Sent>
+void test_permutations() {
+  auto test_prev_permutations = [](auto call_prev_permutation) {
+    auto input = std::array{6, 5, 4, 3, 2, 1};
+    std::array<int, input.size()> last_permutation;
+    for (size_t i = 0; i <= input.size(); ++i) {
+      size_t count = 0;
+
+      bool found_permutation = true;
+      while (found_permutation) {
+        last_permutation = input;
+        std::same_as<std::ranges::prev_permutation_result<Iter>> decltype(auto) ret =
+            call_prev_permutation(Iter(input.data()), Sent(Iter(input.data() + i)));
+        found_permutation = ret.found;
+        assert(base(ret.in) == input.data() + i);
+        if (i > 1) {
+          auto input_subrange            = input | std::views::take(i);
+          auto last_permutation_subrange = last_permutation | std::views::take(i);
+          if (found_permutation)
+            assert(std::ranges::lexicographical_compare(input_subrange, last_permutation_subrange));
+          else
+            assert(std::ranges::lexicographical_compare(last_permutation_subrange, input_subrange));
+        }
+        ++count;
+      }
+      assert(count == factorial(i));
+    }
+    return true;
+  };
+
+  auto iterator_overload = [](auto&& first, auto&& last) { return std::ranges::prev_permutation(first, last); };
+  auto range_overload    = [](auto&& first, auto&& last) {
+    auto range = std::ranges::subrange(first, last);
+    return std::ranges::prev_permutation(range);
+  };
+
+  if constexpr (std::is_same_v<Iter, Sent>) {
+    auto iterator_overload_counted =
+        [](auto first, auto last) -> std::ranges::prev_permutation_result<decltype(first)> {
+      int count = 0;
+      auto ret = std::ranges::prev_permutation(SwapCountingIterator(first, &count), SwapCountingIterator(last, &count));
+      assert(count <= (base(last) - base(first) + 1) / 2);
+      return ret;
+    };
+
+    auto range_overload_counted = [](auto first, auto last) -> std::ranges::prev_permutation_result<decltype(first)> {
+      int count  = 0;
+      auto range = std::ranges::subrange(SwapCountingIterator(first, &count), SwapCountingIterator(last, &count));
+      auto ret   = std::ranges::prev_permutation(range);
+      assert(count <= (base(last) - base(first) + 1) / 2);
+      return ret;
+    };
+
+    test_prev_permutations(iterator_overload_counted);
+    static_assert(test_prev_permutations(iterator_overload_counted));
+    test_prev_permutations(range_overload_counted);
+    static_assert(test_prev_permutations(range_overload_counted));
+  }
+
+  test_prev_permutations(iterator_overload);
+  static_assert(test_prev_permutations(iterator_overload));
+  test_prev_permutations(range_overload);
+  static_assert(test_prev_permutations(range_overload));
+}
+
+template <class Iter>
+void test_sentinels() {
+  test_permutations<Iter, Iter>();
+  test_permutations<Iter, sentinel_wrapper<Iter>>();
+  test_permutations<Iter, sized_sentinel<Iter>>();
+}
+
+void test() {
+  test_sentinels<bidirectional_iterator<int*>>();
+  test_sentinels<random_access_iterator<int*>>();
+  test_sentinels<contiguous_iterator<int*>>();
+  test_sentinels<int*>();
+}
+
+int main(int, char**) { test(); }
diff --git a/libcxx/test/std/algorithms/ranges_result_alias_declarations.compile.pass.cpp b/libcxx/test/std/algorithms/ranges_result_alias_declarations.compile.pass.cpp
--- a/libcxx/test/std/algorithms/ranges_result_alias_declarations.compile.pass.cpp
+++ b/libcxx/test/std/algorithms/ranges_result_alias_declarations.compile.pass.cpp
@@ -56,7 +56,7 @@
 static_assert(std::is_same_v<min_max_result<int>, minmax_result<int>>);
 static_assert(std::is_same_v<min_max_result<int>, minmax_element_result<int>>);
 
-// static_assert(std::is_same_v<in_found_result<int>, next_permutation_result<int>>);
-// static_assert(std::is_same_v<in_found_result<int>, prev_permutation_result<int>>);
+static_assert(std::is_same_v<in_found_result<int>, next_permutation_result<int>>);
+static_assert(std::is_same_v<in_found_result<int>, prev_permutation_result<int>>);
 
 // static_assert(std::is_same_v<out_value_result<int>, iota_result<int>>);
diff --git a/libcxx/test/std/algorithms/ranges_robust_against_nonbool_predicates.compile.pass.cpp b/libcxx/test/std/algorithms/ranges_robust_against_nonbool_predicates.compile.pass.cpp
--- a/libcxx/test/std/algorithms/ranges_robust_against_nonbool_predicates.compile.pass.cpp
+++ b/libcxx/test/std/algorithms/ranges_robust_against_nonbool_predicates.compile.pass.cpp
@@ -167,6 +167,6 @@
   in_pred(std::ranges::push_heap, in, binary_pred);
   in_pred(std::ranges::pop_heap, in, binary_pred);
   in_pred(std::ranges::sort_heap, in, binary_pred);
-  //in_pred(std::ranges::prev_permutation, in, binary_pred);
-  //in_pred(std::ranges::next_permutation, in, binary_pred);
+  in_pred(std::ranges::prev_permutation, in, binary_pred);
+  in_pred(std::ranges::next_permutation, in, binary_pred);
 }
diff --git a/libcxx/test/std/algorithms/ranges_robust_against_omitting_invoke.compile.pass.cpp b/libcxx/test/std/algorithms/ranges_robust_against_omitting_invoke.compile.pass.cpp
--- a/libcxx/test/std/algorithms/ranges_robust_against_omitting_invoke.compile.pass.cpp
+++ b/libcxx/test/std/algorithms/ranges_robust_against_omitting_invoke.compile.pass.cpp
@@ -212,6 +212,6 @@
   in_pred(std::ranges::push_heap, in, &Foo::binary_pred, &Bar::val);
   in_pred(std::ranges::pop_heap, in, &Foo::binary_pred, &Bar::val);
   in_pred(std::ranges::sort_heap, in, &Foo::binary_pred, &Bar::val);
-  //in_pred(std::ranges::prev_permutation, in, &Foo::binary_pred, &Bar::val);
-  //in_pred(std::ranges::next_permutation, in, &Foo::binary_pred, &Bar::val);
+  in_pred(std::ranges::prev_permutation, in, &Foo::binary_pred, &Bar::val);
+  in_pred(std::ranges::next_permutation, in, &Foo::binary_pred, &Bar::val);
 }
diff --git a/libcxx/test/support/almost_satisfies_types.h b/libcxx/test/support/almost_satisfies_types.h
--- a/libcxx/test/support/almost_satisfies_types.h
+++ b/libcxx/test/support/almost_satisfies_types.h
@@ -202,6 +202,10 @@
 };
 
 using BidirectionalRangeNotDerivedFrom = UncheckedRange<BidirectionalIteratorNotDerivedFrom>;
+using BidirectionalRangeNotSentinelSemiregular =
+    UncheckedRange<bidirectional_iterator<int*>, SentinelForNotSemiregular>;
+using BidirectionalRangeNotSentinelWeaklyEqualityComparableWith =
+    UncheckedRange<bidirectional_iterator<int*>, SentinelForNotWeaklyEqualityComparableWith>;
 
 static_assert(std::forward_iterator<BidirectionalIteratorNotDerivedFrom>);
 static_assert(!std::bidirectional_iterator<BidirectionalIteratorNotDerivedFrom>);
diff --git a/libcxx/test/support/test_iterators.h b/libcxx/test/support/test_iterators.h
--- a/libcxx/test/support/test_iterators.h
+++ b/libcxx/test/support/test_iterators.h
@@ -726,6 +726,140 @@
     difference_type stride_displacement_ = 0;
 };
 
+template <std::input_iterator Base>
+consteval auto get_iterator_concept() {
+  if constexpr (std::contiguous_iterator<Base>) {
+    return std::contiguous_iterator_tag();
+  } else if constexpr (std::random_access_iterator<Base>) {
+    return std::random_access_iterator_tag{};
+  } else if constexpr (std::bidirectional_iterator<Base>) {
+    return std::bidirectional_iterator_tag{};
+  } else if constexpr (std::forward_iterator<Base>) {
+    return std::forward_iterator_tag{};
+  } else {
+    return std::input_iterator_tag{};
+  }
+}
+
+template <std::input_iterator Iter>
+using iter_concept_t = decltype(get_iterator_concept<Iter>());
+
+template <class Iter>
+struct SwapCountingIterator {
+  using difference_type  = std::iter_difference_t<Iter>;
+  using value_type       = std::iter_value_t<Iter>;
+  using iterator_concept = iter_concept_t<Iter>;
+
+  Iter iter_;
+  int* counter_;
+  SwapCountingIterator() = default;
+  constexpr SwapCountingIterator(const Iter& iter, int* counter) : iter_(iter), counter_(counter) {}
+
+  constexpr friend void iter_swap(const SwapCountingIterator& lhs, const SwapCountingIterator& rhs) {
+    std::ranges::iter_swap(lhs.iter_, rhs.iter_);
+    ++*lhs.counter_;
+  }
+
+  constexpr SwapCountingIterator& operator++() {
+    ++iter_;
+    return *this;
+  }
+
+  constexpr SwapCountingIterator operator++(int) {
+    auto tmp = *this;
+    ++*this;
+    return tmp;
+  }
+
+  constexpr SwapCountingIterator& operator--() {
+    --iter_;
+    return *this;
+  }
+
+  constexpr SwapCountingIterator operator--(int) {
+    auto tmp = *this;
+    ++*this;
+    return tmp;
+  }
+
+  constexpr auto base() { return base(iter_); }
+
+  constexpr decltype(auto) operator*() const { return *iter_; }
+
+  friend bool operator==(const SwapCountingIterator& lhs, const SwapCountingIterator& rhs) = default;
+
+  constexpr operator Iter() {
+    return iter_;
+  }
+
+  // to satisfy random_access_iterator
+  constexpr SwapCountingIterator& operator+=(difference_type n)
+    requires std::random_access_iterator<Iter> {
+    iter_ += n;
+    return *this;
+  }
+
+  constexpr SwapCountingIterator& operator-=(difference_type n)
+    requires std::random_access_iterator<Iter> {
+    iter_ -= n;
+    return *this;
+  }
+
+  constexpr decltype(auto) operator[](difference_type n) const
+    requires std::random_access_iterator<Iter> {
+    return iter_[n];
+  }
+
+  friend constexpr bool operator<(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires std::random_access_iterator<Iter> {
+    return x.iter_ < y.iter_;
+  }
+
+  friend constexpr bool operator>(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires std::random_access_iterator<Iter> {
+    return x.iter_ > y.iter_;
+  }
+
+  friend constexpr bool operator<=(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires std::random_access_iterator<Iter> {
+    return x.iter_ <= y.iter_;
+  }
+
+  friend constexpr bool operator>=(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires std::random_access_iterator<Iter> {
+    return x.iter_ >= y.iter_;
+  }
+
+  friend constexpr auto operator<=>(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires(std::random_access_iterator<Iter> && std::three_way_comparable<Iter>) {
+    return x.iter_ <=> y.iter_;
+  }
+
+  friend constexpr SwapCountingIterator operator+(const SwapCountingIterator& x, difference_type n)
+    requires std::random_access_iterator<Iter> {
+    return SwapCountingIterator{x.iter_ + n};
+  }
+
+  friend constexpr SwapCountingIterator operator+(difference_type n, const SwapCountingIterator& x)
+    requires std::random_access_iterator<Iter> {
+    return SwapCountingIterator{n + x.iter_};
+  }
+
+  friend constexpr SwapCountingIterator operator-(const SwapCountingIterator& x, difference_type n)
+    requires std::random_access_iterator<Iter> {
+    return SwapCountingIterator{x.iter_ - n};
+  }
+
+  friend constexpr difference_type operator-(const SwapCountingIterator& x, const SwapCountingIterator& y)
+    requires std::random_access_iterator<Iter> {
+    return x.iter_ - y.iter_;
+  }
+
+};
+
+static_assert(std::bidirectional_iterator<SwapCountingIterator<bidirectional_iterator<int*>>>);
+static_assert(std::random_access_iterator<SwapCountingIterator<random_access_iterator<int*>>>);
+
 #endif // TEST_STD_VER > 17
 
 #if TEST_STD_VER > 17
@@ -827,12 +961,12 @@
 // ======================================================================
 // Proxy that can wrap a value or a reference. It simulates C++23's tuple
 // but simplified to just hold one argument.
-// Note that unlike tuple, this class deliberately doesn't have special handling 
-// of swap to cause a compilation error if it's used in an algorithm that relies 
+// Note that unlike tuple, this class deliberately doesn't have special handling
+// of swap to cause a compilation error if it's used in an algorithm that relies
 // on plain swap instead of ranges::iter_swap.
 // This class is useful for testing that if algorithms support proxy iterator
 // properly, i.e. calling ranges::iter_swap and ranges::iter_move instead of
-// plain swap and std::move 
+// plain swap and std::move
 template <class T>
 struct Proxy;
 
@@ -920,29 +1054,16 @@
 template <class Base>
   requires std::derived_from<
       typename std::iterator_traits<Base>::iterator_category,
-      std::input_iterator_tag> 
+      std::input_iterator_tag>
 struct ProxyIteratorBase<Base> {
   using iterator_category = std::input_iterator_tag;
 };
 
-template <std::input_iterator Base>
-consteval auto get_iterator_concept() {
-  if constexpr (std::random_access_iterator<Base>) {
-    return std::random_access_iterator_tag{};
-  } else if constexpr (std::bidirectional_iterator<Base>) {
-    return std::bidirectional_iterator_tag{};
-  } else if constexpr (std::forward_iterator<Base>) {
-    return std::forward_iterator_tag{};
-  } else {
-    return std::input_iterator_tag{};
-  }
-}
-
 template <std::input_iterator Base>
 struct ProxyIterator : ProxyIteratorBase<Base> {
   Base base_;
 
-  using iterator_concept = decltype(get_iterator_concept<Base>());
+  using iterator_concept = iter_concept_t<Base>;
   using value_type       = Proxy<std::iter_value_t<Base>>;
   using difference_type  = std::iter_difference_t<Base>;
 
@@ -951,8 +1072,8 @@
   = default;
 
   constexpr ProxyIterator(Base base) : base_{std::move(base)} {}
-  
-  template <class T> 
+
+  template <class T>
     requires std::constructible_from<Base, T&&>
   constexpr ProxyIterator(T&& t) : base_{std::forward<T>(t)} {}