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
@@ -59,7 +59,7 @@
 Write,sample,Not assigned,n/a,Not started
 Write,unique_copy,Not assigned,n/a,Not started
 Write,partition_copy,Not assigned,n/a,Not started
-Write,partial_sort_copy,Not assigned,n/a,Not started
+Write,partial_sort_copy,Konstantin Varlamov,n/a,In progress
 Merge,merge,Not assigned,n/a,Not started
 Merge,set_difference,Not assigned,n/a,Not started
 Merge,set_intersection,Not assigned,n/a,Not started
@@ -75,7 +75,7 @@
 Permutation,stable_partition,Not assigned,n/a,Not started
 Permutation,sort,Konstantin Varlamov,`D127557 <https://llvm.org/D127557>`_,✅
 Permutation,stable_sort,Konstantin Varlamov,n/a,In progress
-Permutation,partial_sort,Konstantin Varlamov,n/a,In progress
+Permutation,partial_sort,Konstantin Varlamov,`D128744 <https://llvm.org/D128744>`_,✅
 Permutation,nth_element,Not assigned,n/a,Not started
 Permutation,inplace_merge,Not assigned,n/a,Not started
 Permutation,make_heap,Not assigned,n/a,Not started
diff --git a/libcxx/include/CMakeLists.txt b/libcxx/include/CMakeLists.txt
--- a/libcxx/include/CMakeLists.txt
+++ b/libcxx/include/CMakeLists.txt
@@ -102,6 +102,7 @@
   __algorithm/ranges_move.h
   __algorithm/ranges_move_backward.h
   __algorithm/ranges_none_of.h
+  __algorithm/ranges_partial_sort.h
   __algorithm/ranges_replace.h
   __algorithm/ranges_replace_if.h
   __algorithm/ranges_reverse.h
diff --git a/libcxx/include/__algorithm/partial_sort.h b/libcxx/include/__algorithm/partial_sort.h
--- a/libcxx/include/__algorithm/partial_sort.h
+++ b/libcxx/include/__algorithm/partial_sort.h
@@ -17,6 +17,8 @@
 #include <__config>
 #include <__debug>
 #include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__utility/move.h>
 #include <__utility/swap.h>
 
 #if defined(_LIBCPP_DEBUG_RANDOMIZE_UNSPECIFIED_STABILITY)
@@ -29,17 +31,27 @@
 
 _LIBCPP_BEGIN_NAMESPACE_STD
 
-template <class _Compare, class _RandomAccessIterator>
-_LIBCPP_CONSTEXPR_AFTER_CXX17 void
-__partial_sort(_RandomAccessIterator __first, _RandomAccessIterator __middle, _RandomAccessIterator __last,
-               _Compare __comp)
-{
-    if (__first == __middle)
-        return;
+template <class _Compare, class _RandomAccessIterator, class _Sentinel>
+_LIBCPP_HIDE_FROM_ABI constexpr
+_RandomAccessIterator __partial_sort(
+    _RandomAccessIterator __first, _RandomAccessIterator __middle, _Sentinel __last, _Compare __comp) {
+    if (__first == __middle) {
+      if constexpr (is_same<_Sentinel, _RandomAccessIterator>::value) {
+        return __last;
+      } else {
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+        return std::ranges::next(__middle, __last);
+#else
+        static_assert(false, "Before C++20, the end iterator has to have the same type as the begin iterator");
+#endif
+      }
+    }
+
     _VSTD::__make_heap<_Compare>(__first, __middle, __comp);
+
     typename iterator_traits<_RandomAccessIterator>::difference_type __len = __middle - __first;
-    for (_RandomAccessIterator __i = __middle; __i != __last; ++__i)
-    {
+    _RandomAccessIterator __i = __middle;
+    for (; __i != __last; ++__i) {
         if (__comp(*__i, *__first))
         {
             swap(*__i, *__first);
@@ -47,6 +59,37 @@
         }
     }
     _VSTD::__sort_heap<_Compare>(__first, __middle, __comp);
+
+    return __i;
+}
+
+template <class _RandomAccessIterator, class _Sentinel>
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+void __maybe_randomize(_RandomAccessIterator __first, _Sentinel __last) {
+  (void) __first;
+  (void) __last; // In case the randomization is disabled.
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+  _LIBCPP_DEBUG_RANDOMIZE_RANGE(__first, std::ranges::next(__first, __last));
+
+#else
+  static_assert(is_same<_Sentinel, _RandomAccessIterator>::value);
+  _LIBCPP_DEBUG_RANDOMIZE_RANGE(__first, __last);
+#endif
+}
+
+template <class _RandomAccessIterator, class _Sentinel, class _Compare>
+inline _LIBCPP_HIDE_FROM_ABI _LIBCPP_CONSTEXPR_AFTER_CXX17
+_RandomAccessIterator __partial_sort_impl(_RandomAccessIterator __first, _RandomAccessIterator __middle,
+    _Sentinel __last, _Compare& __comp) {
+  std::__maybe_randomize(__first, __last);
+
+  using _Comp_ref = typename __comp_ref_type<_Compare>::type;
+  auto __last_iter = std::__partial_sort<_Comp_ref>(std::move(__first), __middle, __last, __comp);
+
+  std::__maybe_randomize(__middle, __last);
+
+  return __last_iter;
 }
 
 template <class _RandomAccessIterator, class _Compare>
@@ -55,10 +98,7 @@
 partial_sort(_RandomAccessIterator __first, _RandomAccessIterator __middle, _RandomAccessIterator __last,
              _Compare __comp)
 {
-  _LIBCPP_DEBUG_RANDOMIZE_RANGE(__first, __last);
-  typedef typename __comp_ref_type<_Compare>::type _Comp_ref;
-  _VSTD::__partial_sort<_Comp_ref>(__first, __middle, __last, __comp);
-  _LIBCPP_DEBUG_RANDOMIZE_RANGE(__middle, __last);
+  (void)std::__partial_sort_impl(std::move(__first), std::move(__middle), std::move(__last), __comp);
 }
 
 template <class _RandomAccessIterator>
@@ -66,7 +106,7 @@
 void
 partial_sort(_RandomAccessIterator __first, _RandomAccessIterator __middle, _RandomAccessIterator __last)
 {
-    _VSTD::partial_sort(__first, __middle, __last,
+    (void)std::partial_sort(__first, __middle, __last,
                         __less<typename iterator_traits<_RandomAccessIterator>::value_type>());
 }
 
diff --git a/libcxx/include/__algorithm/ranges_partial_sort.h b/libcxx/include/__algorithm/ranges_partial_sort.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_partial_sort.h
@@ -0,0 +1,76 @@
+//===----------------------------------------------------------------------===//
+//
+// 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_PARTIAL_SORT_H
+#define _LIBCPP___ALGORITHM_RANGES_PARTIAL_SORT_H
+
+#include <__algorithm/make_projected.h>
+#include <__algorithm/partial_sort.h>
+#include <__concepts/same_as.h>
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/iterator_traits.h>
+#include <__iterator/next.h>
+#include <__iterator/projected.h>
+#include <__iterator/sortable.h>
+#include <__ranges/access.h>
+#include <__ranges/concepts.h>
+#include <__ranges/dangling.h>
+#include <__utility/forward.h>
+#include <__utility/move.h>
+
+#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
+#  pragma GCC system_header
+#endif
+
+#if _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __partial_sort {
+
+struct __fn {
+  template <class _Iter, class _Sent, class _Comp, class _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Iter __partial_sort_fn_impl(_Iter __first, _Iter __middle, _Sent __last, _Comp& __comp, _Proj& __proj) {
+    auto&& __projected_comp = ranges::__make_projected_comp(__comp, __proj);
+    return std::__partial_sort_impl(std::move(__first), std::move(__middle), __last, __projected_comp);
+  }
+
+  template <random_access_iterator _Iter, sentinel_for<_Iter> _Sent, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<_Iter, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Iter operator()(_Iter __first, _Iter __middle, _Sent __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __partial_sort_fn_impl(std::move(__first), std::move(__middle), std::move(__last), __comp, __proj);
+  }
+
+  template <random_access_range _Range, class _Comp = ranges::less, class _Proj = identity>
+    requires sortable<iterator_t<_Range>, _Comp, _Proj>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Range> operator()(_Range&& __r, iterator_t<_Range> __middle, _Comp __comp = {},
+                                         _Proj __proj = {}) const {
+    return __partial_sort_fn_impl(ranges::begin(__r), std::move(__middle), ranges::end(__r), __comp, __proj);
+  }
+};
+
+} // namespace __partial_sort
+
+inline namespace __cpo {
+  inline constexpr auto partial_sort = __partial_sort::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_STD_VER > 17 && !defined(_LIBCPP_HAS_NO_INCOMPLETE_RANGES)
+
+#endif // _LIBCPP___ALGORITHM_RANGES_PARTIAL_SORT_H
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -286,12 +286,23 @@
             class Proj = identity>
     requires sortable<I, Comp, Proj>
     constexpr I
-      sort(I first, S last, Comp comp = {}, Proj proj = {});                                // since C++20
+      ranges::sort(I first, S last, Comp comp = {}, Proj proj = {});                         // since C++20
 
   template<random_access_range R, class Comp = ranges::less, class Proj = identity>
     requires sortable<iterator_t<R>, Comp, Proj>
     constexpr borrowed_iterator_t<R>
-      sort(R&& r, Comp comp = {}, Proj proj = {});                                          // since C++20
+      ranges::sort(R&& r, Comp comp = {}, Proj proj = {});                                   // since C++20
+
+  template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+           class Proj = identity>
+    requires sortable<I, Comp, Proj>
+    constexpr I
+      ranges::partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});      // since C++20
+
+  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+    requires sortable<iterator_t<R>, Comp, Proj>
+    constexpr borrowed_iterator_t<R>
+      ranges::partial_sort(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});    // since C++20
 
   template<class T, output_iterator<const T&> O, sentinel_for<O> S>
     constexpr O ranges::fill(O first, S last, const T& value);                              // since C++20
@@ -1219,6 +1230,7 @@
 #include <__algorithm/ranges_move.h>
 #include <__algorithm/ranges_move_backward.h>
 #include <__algorithm/ranges_none_of.h>
+#include <__algorithm/ranges_partial_sort.h>
 #include <__algorithm/ranges_replace.h>
 #include <__algorithm/ranges_replace_if.h>
 #include <__algorithm/ranges_reverse.h>
diff --git a/libcxx/include/module.modulemap.in b/libcxx/include/module.modulemap.in
--- a/libcxx/include/module.modulemap.in
+++ b/libcxx/include/module.modulemap.in
@@ -341,6 +341,7 @@
       module ranges_move                     { private header "__algorithm/ranges_move.h" }
       module ranges_move_backward            { private header "__algorithm/ranges_move_backward.h" }
       module ranges_none_of                  { private header "__algorithm/ranges_none_of.h" }
+      module ranges_partial_sort             { private header "__algorithm/ranges_partial_sort.h" }
       module ranges_replace                  { private header "__algorithm/ranges_replace.h" }
       module ranges_replace_if               { private header "__algorithm/ranges_replace_if.h" }
       module ranges_reverse                  { private header "__algorithm/ranges_reverse.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
@@ -171,8 +171,8 @@
     (void)std::ranges::none_of(a, UnaryTrue(&copies)); assert(copies == 0);
     //(void)std::ranges::nth_element(first, mid, last, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::nth_element(a, mid, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::partial_sort(first, mid, last, Less(&copies)); assert(copies == 0);
-    //(void)std::ranges::partial_sort(a, mid, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::partial_sort(first, mid, last, Less(&copies)); assert(copies == 0);
+    (void)std::ranges::partial_sort(a, mid, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(first, last, first2, mid2, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(a, b, Less(&copies)); assert(copies == 0);
     //(void)std::ranges::partition(first, last, 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
@@ -154,8 +154,8 @@
     (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);
     //(void)std::ranges::nth_element(a, mid, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::partial_sort(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
-    //(void)std::ranges::partial_sort(a, mid, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::partial_sort(first, mid, last, Less(), Proj(&copies)); assert(copies == 0);
+    (void)std::ranges::partial_sort(a, mid, Less(), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(first, last, first2, mid2, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partial_sort_copy(a, b, Less(), Proj(&copies), Proj(&copies)); assert(copies == 0);
     //(void)std::ranges::partition(first, last, UnaryTrue(), 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
@@ -139,6 +139,7 @@
 #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_none_of.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_none_of.h'}}
+#include <__algorithm/ranges_partial_sort.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_partial_sort.h'}}
 #include <__algorithm/ranges_replace.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace.h'}}
 #include <__algorithm/ranges_replace_if.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_replace_if.h'}}
 #include <__algorithm/ranges_reverse.h> // expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_reverse.h'}}
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.sort/partial.sort/ranges_partial_sort.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.sort/partial.sort/ranges_partial_sort.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.sort/partial.sort/ranges_partial_sort.pass.cpp
@@ -0,0 +1,290 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// UNSUPPORTED: c++03, c++11, c++14, c++17
+// UNSUPPORTED: libcpp-has-no-incomplete-ranges
+
+// <algorithm>
+
+// template<random_access_iterator I, sentinel_for<I> S, class Comp = ranges::less,
+//           class Proj = identity>
+//    requires sortable<I, Comp, Proj>
+//    constexpr I
+//      ranges::partial_sort(I first, I middle, S last, Comp comp = {}, Proj proj = {});      // since C++20
+//
+//  template<random_access_range R, class Comp = ranges::less, class Proj = identity>
+//    requires sortable<iterator_t<R>, Comp, Proj>
+//    constexpr borrowed_iterator_t<R>
+//      ranges::partial_sort(R&& r, iterator_t<R> middle, Comp comp = {}, Proj proj = {});    // since C++20
+
+#include <algorithm>
+#include <array>
+#include <concepts>
+#include <functional>
+#include <ranges>
+
+#include "almost_satisfies_types.h"
+#include "boolean_testable.h"
+#include "test_iterators.h"
+
+// SFINAE tests.
+
+using BadComparator = ComparatorNotCopyable<int*>;
+static_assert(!std::sortable<int*, BadComparator>);
+
+template <class Iter, class Sent = sentinel_wrapper<Iter>, class Comp = std::ranges::less>
+concept HasPartialSortIt = requires(Iter first, Iter mid, Sent last, Comp comp) {
+  std::ranges::partial_sort(first, mid, last, comp);
+};
+
+static_assert(HasPartialSortIt<int*>);
+static_assert(!HasPartialSortIt<RandomAccessIteratorNotDerivedFrom>);
+static_assert(!HasPartialSortIt<RandomAccessIteratorBadIndex>);
+static_assert(!HasPartialSortIt<int*, SentinelForNotSemiregular>);
+static_assert(!HasPartialSortIt<int*, SentinelForNotWeaklyEqualityComparableWith>);
+static_assert(!HasPartialSortIt<int*, int*, BadComparator>);
+static_assert(!HasPartialSortIt<const int*>); // Doesn't satisfy `sortable`.
+
+template <class Range, class Comp = std::ranges::less>
+concept HasPartialSortR = requires(Range range, std::ranges::iterator_t<Range> mid, Comp comp) {
+  std::ranges::partial_sort(range, mid, comp);
+};
+
+static_assert(HasPartialSortR<UncheckedRange<int*>>);
+static_assert(!HasPartialSortR<RandomAccessRangeNotDerivedFrom>);
+static_assert(!HasPartialSortR<RandomAccessRangeBadIndex>);
+static_assert(!HasPartialSortR<UncheckedRange<int*, SentinelForNotSemiregular>>);
+static_assert(!HasPartialSortR<UncheckedRange<int*, SentinelForNotWeaklyEqualityComparableWith>>);
+static_assert(!HasPartialSortR<UncheckedRange<int*>, BadComparator>);
+static_assert(!HasPartialSortR<UncheckedRange<const int*>>); // Doesn't satisfy `sortable`.
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_one(std::array<int, N> input, size_t mid_index, std::array<int, N> expected) {
+  { // (iterator, sentinel) overload.
+    auto partially_sorted = input;
+    auto b = Iter(partially_sorted.data());
+    auto m = b + mid_index;
+    auto e = Sent(Iter(partially_sorted.data() + partially_sorted.size()));
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::partial_sort(b, m, e);
+    assert(std::equal(partially_sorted.begin(), partially_sorted.begin() + mid_index, expected.begin(),
+          expected.begin() + mid_index));
+    assert(base(last) == partially_sorted.data() + partially_sorted.size());
+  }
+
+  { // (range) overload.
+    auto partially_sorted = input;
+    auto b = Iter(partially_sorted.data());
+    auto m = b + mid_index;
+    auto e = Sent(Iter(partially_sorted.data() + partially_sorted.size()));
+    auto range = std::ranges::subrange(b, e);
+
+    std::same_as<Iter> decltype(auto) last = std::ranges::partial_sort(range, m);
+    assert(std::equal(partially_sorted.begin(), partially_sorted.begin() + mid_index, expected.begin(),
+          expected.begin() + mid_index));
+    assert(base(last) == partially_sorted.data() + partially_sorted.size());
+  }
+}
+
+template <class Iter, class Sent, size_t N>
+constexpr void test_all_cases(std::array<int, N> input) {
+  auto sorted = input;
+  std::sort(sorted.begin(), sorted.end());
+
+  for (size_t n = 0; n <= N; ++n) {
+    test_one<Iter, Sent, N>(input, n, sorted);
+  }
+}
+
+constexpr void test_iterators() {
+  auto check = []<class Iter, class Sent> {
+    // Empty sequence.
+    test_one<Iter, Sent, 0>({}, 0, {});
+
+    // 1-element sequence.
+    test_all_cases<Iter, Sent>(std::array{1});
+
+    // 2-element sequence.
+    test_all_cases<Iter, Sent>(std::array{2, 1});
+
+    // 3-element sequence.
+    test_all_cases<Iter, Sent>(std::array{2, 1, 3});
+
+    // Longer sequence.
+    test_all_cases<Iter, Sent>(std::array{2, 1, 3, 6, 8, 4, 11, 5});
+
+    // Longer sequence with duplicates.
+    test_all_cases<Iter, Sent>(std::array{2, 1, 3, 6, 2, 8, 6});
+
+    // All elements are the same.
+    test_all_cases<Iter, Sent>(std::array{1, 1, 1});
+
+    // Already sorted.
+    test_all_cases<Iter, Sent>(std::array{1, 2, 3, 4, 5});
+
+    // Descending.
+    test_all_cases<Iter, Sent>(std::array{5, 4, 3, 2, 1});
+
+    // Repeating pattern.
+    test_all_cases<Iter, Sent>(std::array{1, 2, 1, 2, 1, 2});
+  };
+
+  check.operator()<random_access_iterator<int*>, random_access_iterator<int*>>();
+  check.operator()<random_access_iterator<int*>, sentinel_wrapper<random_access_iterator<int*>>>();
+  check.operator()<contiguous_iterator<int*>, contiguous_iterator<int*>>();
+  check.operator()<contiguous_iterator<int*>, sentinel_wrapper<contiguous_iterator<int*>>>();
+  check.operator()<int*, int*>();
+  check.operator()<int*, sentinel_wrapper<int*>>();
+}
+
+constexpr bool test() {
+  test_iterators();
+
+  { // A custom comparator works.
+    const std::array orig_in = {1, 2, 3, 4, 5};
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(b, m, in.end(), std::ranges::greater{});
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{5, 4}
+      ));
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(in, m, std::ranges::greater{});
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{5, 4}
+      ));
+      assert(last == in.end());
+    }
+  }
+
+  { // A custom projection works.
+    struct A {
+      int a;
+      constexpr bool operator==(const A&) const = default;
+    };
+
+    const std::array orig_in = {A{2}, A{3}, A{1}};
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(b, m, in.end(), {}, &A::a);
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{A{1}, A{2}}
+      ));
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(in, m, {}, &A::a);
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{A{1}, A{2}}
+      ));
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::invoke` is used in the implementation.
+    struct S {
+      int i;
+      constexpr S(int i_) : i(i_) {}
+
+      constexpr bool comparator(const S& rhs) const { return i < rhs.i; }
+      constexpr const S& projection() const { return *this; }
+
+      constexpr bool operator==(const S&) const = default;
+    };
+
+    const std::array orig_in = {S{2}, S{3}, S{1}};
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(b, m, in.end(), &S::comparator, &S::projection);
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{S{1}, S{2}}
+      ));
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(in, m, &S::comparator, &S::projection);
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{S{1}, S{2}}
+      ));
+      assert(last == in.end());
+    }
+  }
+
+  { // The comparator can return any type that's convertible to `bool`.
+    const std::array orig_in = {2, 1, 3};
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(b, m, in.end(),
+          [](int i, int j) { return BooleanTestable{i < j}; });
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{1, 2}
+      ));
+      assert(last == in.end());
+    }
+
+    {
+      auto in = orig_in;
+      auto b = in.begin();
+      auto m = b + 2;
+
+      auto last = std::ranges::partial_sort(in, m,
+          [](int i, int j) { return BooleanTestable{i < j}; });
+      assert(std::ranges::equal(
+          std::ranges::subrange(b, m), std::array{1, 2}
+      ));
+      assert(last == in.end());
+    }
+  }
+
+  { // `std::ranges::dangling` is returned.
+    static_assert(std::same_as<std::ranges::dangling,
+        decltype(std::ranges::partial_sort(UncheckedRange<int*>(), nullptr))>);
+  }
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
diff --git a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
--- a/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
+++ b/libcxx/test/std/library/description/conventions/customization.point.object/niebloid.compile.pass.cpp
@@ -109,7 +109,7 @@
 //static_assert(test(std::ranges::next_permutation, a));
 static_assert(test(std::ranges::none_of, a, odd));
 //static_assert(test(std::ranges::nth_element, a, a+5));
-//static_assert(test(std::ranges::partial_sort, a, a+5));
+static_assert(test(std::ranges::partial_sort, a, a+5));
 //static_assert(test(std::ranges::partial_sort_copy, a, a));
 //static_assert(test(std::ranges::partition, a, odd));
 //static_assert(test(std::ranges::partition_copy, a, a, a, odd));