diff --git a/libcxx/include/__iterator/concepts.h b/libcxx/include/__iterator/concepts.h
--- a/libcxx/include/__iterator/concepts.h
+++ b/libcxx/include/__iterator/concepts.h
@@ -112,6 +112,16 @@
   incrementable<_Ip> &&
   sentinel_for<_Ip, _Ip>;
 
+// [iterator.concept.bidir]
+template<class _Ip>
+concept bidirectional_iterator =
+  forward_iterator<_Ip> &&
+  derived_from<_ITER_CONCEPT<_Ip>, bidirectional_iterator_tag> &&
+  requires(_Ip __i) {
+    { --__i } -> same_as<_Ip&>;
+    { __i-- } -> same_as<_Ip>;
+  };
+
 // clang-format on
 
 #endif // !defined(_LIBCPP_HAS_NO_RANGES)
diff --git a/libcxx/include/__ranges/concepts.h b/libcxx/include/__ranges/concepts.h
--- a/libcxx/include/__ranges/concepts.h
+++ b/libcxx/include/__ranges/concepts.h
@@ -58,6 +58,9 @@
 template <class _Tp>
 concept forward_range = input_range<_Tp>&& forward_iterator<iterator_t<_Tp> >;
 
+template <class _Tp>
+concept bidirectional_range =
+    forward_range<_Tp>&& bidirectional_iterator<iterator_t<_Tp> >;
 } // namespace ranges
 
 #endif // !defined(_LIBCPP_HAS_NO_RANGES)
diff --git a/libcxx/include/iterator b/libcxx/include/iterator
--- a/libcxx/include/iterator
+++ b/libcxx/include/iterator
@@ -76,6 +76,10 @@
 template<class I>
   concept forward_iterator = see below;                    // since C++20
 
+// [iterator.concept.bidir], concept bidirectional_iterator
+template<class I>
+  concept bidirectional_­iterator = see below;              // since C++20
+
 template<class Category, class T, class Distance = ptrdiff_t,
          class Pointer = T*, class Reference = T&>
 struct iterator
diff --git a/libcxx/include/ranges b/libcxx/include/ranges
--- a/libcxx/include/ranges
+++ b/libcxx/include/ranges
@@ -50,6 +50,9 @@
 
   template<class T>
     concept forward_range = see below;
+
+  template<class T>
+  concept bidirectional_­range = see below;
 }
 
 */
diff --git a/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/bidirectional_iterator.compile.pass.cpp
@@ -0,0 +1,258 @@
+//===----------------------------------------------------------------------===//
+//
+// 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-no-concepts
+// UNSUPPORTED: gcc-10
+
+// template<class T>
+// concept bidirectional_iterator;
+
+#include <iterator>
+
+#include <array>
+#include <concepts>
+#include <deque>
+#ifndef _LIBCPP_HAS_NO_FILESYSTEM_LIBRARY
+#include <filesystem>
+#endif
+#include <forward_list>
+#include <list>
+#include <map>
+#include <memory>
+#include <set>
+#include <string>
+#include <string_view>
+#include <optional>
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+
+#include "test_iterators.h"
+
+namespace standard_types {
+static_assert(std::bidirectional_iterator<int*>);
+static_assert(std::bidirectional_iterator<int const*>);
+static_assert(std::bidirectional_iterator<int volatile*>);
+static_assert(std::bidirectional_iterator<int const volatile*>);
+
+// <array>
+static_assert(std::bidirectional_iterator<std::array<int, 10>::iterator>);
+static_assert(std::bidirectional_iterator<std::array<int, 10>::const_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::array<int, 10>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::array<int, 10>::const_reverse_iterator>);
+
+// <deque>
+static_assert(std::bidirectional_iterator<std::deque<int>::iterator>);
+static_assert(std::bidirectional_iterator<std::deque<int>::const_iterator>);
+static_assert(std::bidirectional_iterator<std::deque<int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::deque<int>::const_reverse_iterator>);
+
+// <forward_list>
+static_assert(!std::bidirectional_iterator<std::forward_list<int>::iterator>);
+static_assert(
+    !std::bidirectional_iterator<std::forward_list<int>::const_iterator>);
+
+// <list>
+static_assert(std::bidirectional_iterator<std::list<int>::iterator>);
+static_assert(std::bidirectional_iterator<std::list<int>::const_iterator>);
+static_assert(std::bidirectional_iterator<std::list<int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::list<int>::const_reverse_iterator>);
+
+// <map>
+static_assert(std::bidirectional_iterator<std::map<int, int>::iterator>);
+static_assert(std::bidirectional_iterator<std::map<int, int>::const_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::map<int, int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::map<int, int>::const_reverse_iterator>);
+
+static_assert(std::bidirectional_iterator<std::multimap<int, int>::iterator>);
+static_assert(
+    std::bidirectional_iterator<std::multimap<int, int>::const_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::multimap<int, int>::reverse_iterator>);
+static_assert(std::bidirectional_iterator<
+              std::multimap<int, int>::const_reverse_iterator>);
+
+// <set>
+static_assert(std::bidirectional_iterator<std::set<int>::iterator>);
+static_assert(std::bidirectional_iterator<std::set<int>::const_iterator>);
+static_assert(std::bidirectional_iterator<std::set<int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::set<int>::const_reverse_iterator>);
+
+static_assert(std::bidirectional_iterator<std::multiset<int>::iterator>);
+static_assert(std::bidirectional_iterator<std::multiset<int>::const_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::multiset<int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::multiset<int>::const_reverse_iterator>);
+
+// <string>
+static_assert(std::bidirectional_iterator<std::string::iterator>);
+static_assert(std::bidirectional_iterator<std::string::const_iterator>);
+static_assert(std::bidirectional_iterator<std::string::reverse_iterator>);
+static_assert(std::bidirectional_iterator<std::string::const_reverse_iterator>);
+
+// <string_view>
+static_assert(std::bidirectional_iterator<std::string_view::iterator>);
+static_assert(std::bidirectional_iterator<std::string_view::const_iterator>);
+static_assert(std::bidirectional_iterator<std::string_view::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::string_view::const_reverse_iterator>);
+
+// <unordered_map>
+static_assert(
+    !std::bidirectional_iterator<std::unordered_map<int, int>::iterator>);
+static_assert(
+    !std::bidirectional_iterator<std::unordered_map<int, int>::const_iterator>);
+
+static_assert(
+    !std::bidirectional_iterator<std::unordered_multimap<int, int>::iterator>);
+static_assert(!std::bidirectional_iterator<
+              std::unordered_multimap<int, int>::const_iterator>);
+
+// <unordered_set>
+static_assert(!std::bidirectional_iterator<std::unordered_set<int>::iterator>);
+static_assert(
+    !std::bidirectional_iterator<std::unordered_set<int>::const_iterator>);
+
+static_assert(
+    !std::bidirectional_iterator<std::unordered_multiset<int, int>::iterator>);
+static_assert(!std::bidirectional_iterator<
+              std::unordered_multiset<int, int>::const_iterator>);
+
+// <vector>
+static_assert(std::bidirectional_iterator<std::vector<int>::iterator>);
+static_assert(std::bidirectional_iterator<std::vector<int>::const_iterator>);
+static_assert(std::bidirectional_iterator<std::vector<int>::reverse_iterator>);
+static_assert(
+    std::bidirectional_iterator<std::vector<int>::const_reverse_iterator>);
+} // namespace standard_types
+
+struct not_forward_iterator {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type operator*() const;
+
+  not_forward_iterator& operator++();
+  not_forward_iterator operator++(int);
+
+  not_forward_iterator& operator--();
+  not_forward_iterator& operator--(int);
+};
+static_assert(std::input_iterator<not_forward_iterator> &&
+              !std::forward_iterator<not_forward_iterator> &&
+              !std::bidirectional_iterator<not_forward_iterator>);
+
+struct wrong_iterator_category {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_category = std::forward_iterator_tag;
+
+  value_type& operator*() const;
+
+  wrong_iterator_category& operator++();
+  wrong_iterator_category operator++(int);
+
+  wrong_iterator_category& operator--();
+  wrong_iterator_category operator--(int);
+
+  bool operator==(wrong_iterator_category const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<wrong_iterator_category>);
+
+struct wrong_iterator_concept {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::forward_iterator_tag;
+
+  value_type& operator*() const;
+
+  wrong_iterator_concept& operator++();
+  wrong_iterator_concept operator++(int);
+
+  wrong_iterator_concept& operator--();
+  wrong_iterator_concept operator--(int);
+
+  bool operator==(wrong_iterator_concept const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<wrong_iterator_concept>);
+
+struct no_predecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  no_predecrement& operator++();
+  no_predecrement operator++(int);
+
+  no_predecrement operator--(int);
+
+  bool operator==(no_predecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<no_predecrement>);
+
+struct bad_predecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  bad_predecrement& operator++();
+  bad_predecrement operator++(int);
+
+  bad_predecrement operator--();
+  bad_predecrement operator--(int);
+
+  bool operator==(bad_predecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<bad_predecrement>);
+
+struct no_postdecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  no_postdecrement& operator++();
+  no_postdecrement operator++(int);
+
+  no_postdecrement& operator--();
+
+  bool operator==(no_postdecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<no_postdecrement>);
+
+struct bad_postdecrement {
+  using value_type = int;
+  using difference_type = std::ptrdiff_t;
+  using iterator_concept = std::bidirectional_iterator_tag;
+
+  value_type& operator*() const;
+
+  bad_postdecrement& operator++();
+  bad_postdecrement operator++(int);
+
+  bad_postdecrement& operator--();
+  bad_postdecrement& operator--(int);
+
+  bool operator==(bad_postdecrement const&) const = default;
+};
+static_assert(!std::bidirectional_iterator<bad_postdecrement>);
diff --git a/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/iterators/iterator.requirements/iterator.concepts/iterator.concept.bidir/subsumption.compile.pass.cpp
@@ -0,0 +1,33 @@
+//===----------------------------------------------------------------------===//
+//
+// 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-no-concepts
+// UNSUPPORTED: gcc-10
+
+// template<class T>
+// concept bidirectional_iterator;
+
+#include <iterator>
+
+#include <concepts>
+
+// clang-format off
+template<std::forward_iterator I>
+requires std::derived_from<std::_ITER_CONCEPT<I>, std::bidirectional_iterator_tag>
+[[nodiscard]] constexpr bool check_subsumption() {
+  return false;
+}
+
+template<std::bidirectional_iterator>
+[[nodiscard]] constexpr bool check_subsumption() {
+  return true;
+}
+// clang-format on
+
+static_assert(check_subsumption<int*>());
diff --git a/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp b/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/ranges/range.refinements/bidirectional_range.compile.pass.cpp
@@ -0,0 +1,74 @@
+//===----------------------------------------------------------------------===//
+//
+// 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-no-concepts
+// UNSUPPORTED: gcc-10
+
+// template<range _Rp>
+// concept bidirectional_range;
+
+#include <ranges>
+
+#include <array>
+#include <deque>
+#include <forward_list>
+#include <list>
+#include <map>
+#include <set>
+#include <string>
+#include <string_view>
+#include <unordered_map>
+#include <unordered_set>
+#include <vector>
+
+#include "test_range.h"
+
+namespace stdr = std::ranges;
+
+static_assert(stdr::bidirectional_range<std::array<int, 10> >);
+static_assert(stdr::bidirectional_range<std::deque<int> >);
+static_assert(!stdr::bidirectional_range<std::forward_list<int> >);
+static_assert(stdr::bidirectional_range<std::list<int> >);
+static_assert(stdr::bidirectional_range<std::map<int, long> >);
+static_assert(stdr::bidirectional_range<std::multimap<int, long> >);
+static_assert(stdr::bidirectional_range<std::multiset<int> >);
+static_assert(stdr::bidirectional_range<std::set<int> >);
+static_assert(stdr::bidirectional_range<std::string>);
+static_assert(stdr::bidirectional_range<std::string_view>);
+static_assert(!stdr::bidirectional_range<std::unordered_map<int, long> >);
+static_assert(!stdr::bidirectional_range<std::unordered_multimap<int, long> >);
+static_assert(!stdr::bidirectional_range<std::unordered_multiset<int> >);
+static_assert(!stdr::bidirectional_range<std::unordered_set<int> >);
+static_assert(stdr::bidirectional_range<std::vector<int> >);
+
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::array<int, 10> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::deque<int> > >);
+static_assert(stdr::bidirectional_range<bidirectional_range<std::list<int> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::map<int, long> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::multimap<int, long> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::multiset<int> > >);
+static_assert(stdr::bidirectional_range<bidirectional_range<std::set<int> > >);
+static_assert(stdr::bidirectional_range<bidirectional_range<std::string> >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::string_view> >);
+static_assert(stdr::bidirectional_range<
+              bidirectional_range<std::unordered_map<int, long> > >);
+static_assert(stdr::bidirectional_range<
+              bidirectional_range<std::unordered_multimap<int, long> > >);
+static_assert(stdr::bidirectional_range<
+              bidirectional_range<std::unordered_multiset<int> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::unordered_set<int> > >);
+static_assert(
+    stdr::bidirectional_range<bidirectional_range<std::vector<int> > >);
diff --git a/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp b/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
--- a/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
+++ b/libcxx/test/std/ranges/range.refinements/subsumption.compile.pass.cpp
@@ -53,3 +53,19 @@
 // clang-format on
 
 static_assert(check_forward_range_subsumption<range>());
+
+// clang-format off
+template<std::ranges::forward_range R>
+requires std::bidirectional_iterator<std::ranges::iterator_t<R> >
+[[nodiscard]] constexpr bool check_bidirectional_range_subsumption() {
+  return false;
+}
+
+template<std::ranges::bidirectional_range>
+requires true
+[[nodiscard]] constexpr bool check_bidirectional_range_subsumption() {
+  return true;
+}
+// clang-format on
+
+static_assert(check_bidirectional_range_subsumption<range>());
diff --git a/libcxx/test/support/test_range.h b/libcxx/test/support/test_range.h
--- a/libcxx/test/support/test_range.h
+++ b/libcxx/test/support/test_range.h
@@ -43,4 +43,12 @@
   sentinel end() const;
 };
 
+template <class R>
+struct bidirectional_range {
+  bidirectional_iterator<std::ranges::iterator_t<R> > begin();
+  bidirectional_iterator<std::ranges::iterator_t<R const> > begin() const;
+  sentinel end();
+  sentinel end() const;
+};
+
 #endif // LIBCXX_TEST_SUPPORT_TEST_RANGE_H