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
@@ -19,7 +19,7 @@
 Search,max,Not assigned,n/a,Not started
 Search,minmax,Not assigned,n/a,Not started
 Search,min_element,Not assigned,n/a,Not started
-Search,max_element,Not assigned,n/a,Not started
+Search,max_element,Nikolas Klauser,n/a,Complete
 Search,minmax_element,Not assigned,n/a,Not started
 Search,count,Not assigned,n/a,Not started
 Search,count_if,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
@@ -61,6 +61,7 @@
   __algorithm/pop_heap.h
   __algorithm/prev_permutation.h
   __algorithm/push_heap.h
+  __algorithm/ranges_max_element.h
   __algorithm/remove.h
   __algorithm/remove_copy.h
   __algorithm/remove_copy_if.h
diff --git a/libcxx/include/__algorithm/ranges_max_element.h b/libcxx/include/__algorithm/ranges_max_element.h
new file mode 100644
--- /dev/null
+++ b/libcxx/include/__algorithm/ranges_max_element.h
@@ -0,0 +1,72 @@
+//===----------------------------------------------------------------------===//
+//
+// 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_MAX_ELEMENT_H
+#define _LIBCPP___ALGORITHM_RANGES_MAX_ELEMENT_H
+
+#include <__config>
+#include <__functional/identity.h>
+#include <__functional/invoke.h>
+#include <__functional/ranges_operations.h>
+#include <__iterator/concepts.h>
+#include <__iterator/projected.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
+
+#ifndef _LIBCPP_HAS_NO_RANGES
+
+_LIBCPP_BEGIN_NAMESPACE_STD
+
+namespace ranges {
+namespace __max_element {
+struct __fn {
+
+  template <class _Ip, class _Sp, class _Proj, class _Comp>
+  _LIBCPP_HIDE_FROM_ABI constexpr static
+  _Ip __go(_Ip __first, _Sp __last, _Comp& __comp, _Proj& __proj) {
+    if (__first == __last)
+      return __first;
+
+    _Ip __i = __first;
+    while (++__i != __last)
+      if (bool(_VSTD::invoke(__comp, _VSTD::invoke(__proj, *__first), _VSTD::invoke(__proj, *__i))))
+        __first = __i;
+    return __first;
+  }
+
+  template <forward_iterator _Ip, sentinel_for<_Ip> _Sp, class _Proj = identity,
+            indirect_strict_weak_order<projected<_Ip, _Proj>> _Comp = ranges::less>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  _Ip operator()(_Ip __first, _Sp __last, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __go(__first, __last, __comp, __proj);
+  }
+
+  template <forward_range _Rp, class _Proj = identity,
+            indirect_strict_weak_order<projected<iterator_t<_Rp>, _Proj>> _Comp = ranges::less>
+  _LIBCPP_HIDE_FROM_ABI constexpr
+  borrowed_iterator_t<_Rp> operator()(_Rp&& __r, _Comp __comp = {}, _Proj __proj = {}) const {
+    return __go(ranges::begin(__r), ranges::end(__r), __comp, __proj);
+  }
+};
+} // namespace __max_element
+
+inline namespace __cpo {
+  inline constexpr auto max_element = __max_element::__fn{};
+} // namespace __cpo
+} // namespace ranges
+
+_LIBCPP_END_NAMESPACE_STD
+
+#endif // _LIBCPP_HAS_NO_RANGES
+
+#endif // _LIBCPP___ALGORITHM_RANGES_MAX_ELEMENT_H
diff --git a/libcxx/include/algorithm b/libcxx/include/algorithm
--- a/libcxx/include/algorithm
+++ b/libcxx/include/algorithm
@@ -731,6 +731,7 @@
 #include <__algorithm/pop_heap.h>
 #include <__algorithm/prev_permutation.h>
 #include <__algorithm/push_heap.h>
+#include <__algorithm/ranges_max_element.h>
 #include <__algorithm/remove.h>
 #include <__algorithm/remove_copy.h>
 #include <__algorithm/remove_copy_if.h>
diff --git a/libcxx/include/module.modulemap b/libcxx/include/module.modulemap
--- a/libcxx/include/module.modulemap
+++ b/libcxx/include/module.modulemap
@@ -281,6 +281,7 @@
       module pop_heap                 { private header "__algorithm/pop_heap.h" }
       module prev_permutation         { private header "__algorithm/prev_permutation.h" }
       module push_heap                { private header "__algorithm/push_heap.h" }
+      module ranges_max_element       { private header "__algorithm/ranges_max_element.h" }
       module remove                   { private header "__algorithm/remove.h" }
       module remove_copy              { private header "__algorithm/remove_copy.h" }
       module remove_copy_if           { private header "__algorithm/remove_copy_if.h" }
diff --git a/libcxx/test/libcxx/diagnostics/detail.headers/algorithm/ranges_max_element.module.verify.cpp b/libcxx/test/libcxx/diagnostics/detail.headers/algorithm/ranges_max_element.module.verify.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/libcxx/diagnostics/detail.headers/algorithm/ranges_max_element.module.verify.cpp
@@ -0,0 +1,15 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+// REQUIRES: modules-build
+
+// WARNING: This test was generated by 'generate_private_header_tests.py'
+// and should not be edited manually.
+
+// expected-error@*:* {{use of private header from outside its module: '__algorithm/ranges_max_element.h'}}
+#include <__algorithm/ranges_max_element.h>
diff --git a/libcxx/test/std/algorithms/alg.sorting/alg.min.max/ranges.max_element.pass.cpp b/libcxx/test/std/algorithms/alg.sorting/alg.min.max/ranges.max_element.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/algorithms/alg.sorting/alg.min.max/ranges.max_element.pass.cpp
@@ -0,0 +1,150 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+//  template<forward_iterator I, sentinel_for<I> S, class Proj = identity,
+//    indirect_strict_weak_order<projected<I, Proj>> Comp = ranges::less>
+//  constexpr I ranges::max_element(I first, S last, Comp comp = {}, Proj proj = {});
+//
+//  template<forward_range R, class Proj = identity,
+//    indirect_strict_weak_order<projected<iterator_t<R>, Proj>> Comp = ranges::less>
+//  constexpr borrowed_iterator_t<R> ranges::max_element(R&& r, Comp comp = {}, Proj proj = {});
+
+#include <algorithm>
+#include <array>
+#include <cassert>
+#include <random>
+#include <ranges>
+
+#include "test_macros.h"
+#include "test_iterators.h"
+
+template <class T>
+concept MinElementCallable = requires (T i) { std::ranges::max_element(i); };
+
+struct NoLessThanOp {};
+struct NotTotallyOrdered {
+  int i;
+  bool operator<(const NotTotallyOrdered& o) const { return i < o.i; }
+};
+
+static_assert(MinElementCallable<std::array<int, 0>>);
+static_assert(!MinElementCallable<int>);
+static_assert(!MinElementCallable<NoLessThanOp>);
+static_assert(!MinElementCallable<NotTotallyOrdered>);
+
+template <class Iter>
+constexpr void test_iterators(Iter first, Iter last) {
+  std::same_as<Iter> auto it = std::ranges::max_element(first, last);
+  if (first != last) {
+    for (Iter j = first; j != last; ++j)
+      assert(!(*it < *j));
+  } else {
+    assert(it == first);
+  }
+}
+
+template <class Range, class Iter>
+constexpr void test_range(Range&& rng, Iter begin, Iter end) {
+  std::same_as<Iter> auto it = std::ranges::max_element(std::forward<Range>(rng));
+  if (begin != end) {
+    for (Iter j = begin; j != end; ++j)
+      assert(!(*it < *j));
+  } else {
+    assert(it == begin);
+  }
+}
+
+template <size_t N, class... Iters>
+constexpr void test(std::array<int, N> a) {
+  (test_iterators(Iters(a.begin()), Iters(a.end())), ...);
+  test_range(a, a.begin(), a.end());
+}
+
+template <class... Iters>
+constexpr bool test() {
+  test<0, Iters...>({});
+  test<1, Iters...>({1});
+  test<2, Iters...>({1, 2});
+  test<2, Iters...>({2, 1});
+  test<3, Iters...>({2, 1, 2});
+  test<3, Iters...>({2, 1, 1});
+
+  return true;
+}
+
+constexpr void test_borrowed_range_and_sentinel() {
+  int a[] = {7, 6, 1, 3, 5, 1, 2, 4};
+
+  std::ranges::subrange sr {a, sentinel_wrapper(a + 8)};
+  int* ret = std::ranges::max_element(sr);
+  assert(ret == a);
+}
+
+constexpr void test_comparator() {
+    int a[] = {7, 6, 9, 3, 5, 1, 2, 4};
+
+  std::ranges::subrange sr {a, sentinel_wrapper(a + 8)};
+  int* ret = std::ranges::max_element(sr, std::ranges::greater{});
+  assert(ret == a + 5);
+}
+
+constexpr void test_projection() {
+  int a[] = {7, 6, 9, 3, 5, 1, 2, 4};
+
+  std::ranges::subrange sr {a, sentinel_wrapper(a + 8)};
+  int* ret = std::ranges::max_element(sr, std::ranges::less{}, [](int i){ return i == 1 ? 100 : i; });
+  assert(ret == a + 5);
+}
+
+struct Immobile {
+  int i;
+
+  constexpr Immobile(int i_) : i(i_) {}
+  Immobile(const Immobile&) = delete;
+  Immobile(Immobile&&) = delete;
+
+  auto operator<=>(const Immobile&) const = default;
+};
+
+constexpr void test_immobile() {
+  Immobile arr[] {1, 2, 3};
+  assert(std::ranges::max_element(arr) == arr);
+  assert(std::ranges::max_element(arr, arr + 3) == arr);
+}
+
+static_assert(std::is_same_v<std::ranges::dangling, decltype(std::ranges::max_element(std::array<int, 0>{}))>);
+
+constexpr bool test() {
+
+  test<forward_iterator<const int*>,
+       bidirectional_iterator<const int*>,
+       random_access_iterator<const int*>,
+       const int*>();
+
+  int a[] = {7, 6, 5, 3, 4, 2, 1, 8};
+  test_iterators(a, a + 8);
+  int a2[] = {7, 6, 5, 3, 4, 2, 1, 8};
+  test_range(a2, a2, a2 + 8);
+
+  test_borrowed_range_and_sentinel();
+  test_comparator();
+  test_projection();
+
+  return true;
+}
+
+int main(int, char**) {
+  test();
+  static_assert(test());
+
+  return 0;
+}
\ No newline at end of file