diff --git a/libcxx/docs/Status/SpaceshipProjects.csv b/libcxx/docs/Status/SpaceshipProjects.csv
--- a/libcxx/docs/Status/SpaceshipProjects.csv
+++ b/libcxx/docs/Status/SpaceshipProjects.csv
@@ -21,8 +21,8 @@
 | `[tuple.rel] <https://wg21.link/tuple.rel>`_,| `tuple <https://reviews.llvm.org/D108250>`_,[expos.only.func],Kent Ross,|Complete|
 "| `[optional.relops] <https://wg21.link/optional.relops>`_
 | `[optional.nullops] <https://wg21.link/optional.nullops>`_
-| `[optional.comp.with.t] <https://wg21.link/optional.comp.with.t>`_","| optional
-| nullopt",None,Kent Ross,|In Progress|
+| `[optional.comp.with.t] <https://wg21.link/optional.comp.with.t>`_","| `optional <https://reviews.llvm.org/D146392>`_
+| `nullopt <https://reviews.llvm.org/D146392>`_",None,Hristo Hristov,|Complete|
 "| `[variant.relops] <https://wg21.link/variant.relops>`_
 | `[variant.monostate.relops] <https://wg21.link/variant.monostate.relops>`_","| `monostate <https://reviews.llvm.org/D131372>`_
 | `variant <https://reviews.llvm.org/D131372>`_",None,Kent Ross,|Complete|
diff --git a/libcxx/include/optional b/libcxx/include/optional
--- a/libcxx/include/optional
+++ b/libcxx/include/optional
@@ -16,107 +16,125 @@
 // C++1z
 
 namespace std {
-  // 23.6.3, optional for object types
+  // [optional.optional], class template optional
   template <class T> class optional;
 
-  // 23.6.4, no-value state indicator
+  // [optional.nullopt], no-value state indicator
   struct nullopt_t{see below };
   inline constexpr nullopt_t nullopt(unspecified );
 
-  // 23.6.5, class bad_optional_access
+  // [optional.bad.access], class bad_optional_access
   class bad_optional_access;
 
-  // 23.6.6, relational operators
+  // [optional.relops], relational operators
   template <class T, class U>
-  constexpr bool operator==(const optional<T>&, const optional<U>&);
+    constexpr bool operator==(const optional<T>&, const optional<U>&);
   template <class T, class U>
-  constexpr bool operator!=(const optional<T>&, const optional<U>&);
+    constexpr bool operator!=(const optional<T>&, const optional<U>&);
   template <class T, class U>
-  constexpr bool operator<(const optional<T>&, const optional<U>&);
+    constexpr bool operator<(const optional<T>&, const optional<U>&);
   template <class T, class U>
-  constexpr bool operator>(const optional<T>&, const optional<U>&);
+    constexpr bool operator>(const optional<T>&, const optional<U>&);
   template <class T, class U>
-  constexpr bool operator<=(const optional<T>&, const optional<U>&);
+    constexpr bool operator<=(const optional<T>&, const optional<U>&);
   template <class T, class U>
-  constexpr bool operator>=(const optional<T>&, const optional<U>&);
-
-  // 23.6.7 comparison with nullopt
-  template <class T> constexpr bool operator==(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator==(nullopt_t, const optional<T>&) noexcept;
-  template <class T> constexpr bool operator!=(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator!=(nullopt_t, const optional<T>&) noexcept;
-  template <class T> constexpr bool operator<(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator<(nullopt_t, const optional<T>&) noexcept;
-  template <class T> constexpr bool operator<=(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator<=(nullopt_t, const optional<T>&) noexcept;
-  template <class T> constexpr bool operator>(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator>(nullopt_t, const optional<T>&) noexcept;
-  template <class T> constexpr bool operator>=(const optional<T>&, nullopt_t) noexcept;
-  template <class T> constexpr bool operator>=(nullopt_t, const optional<T>&) noexcept;
-
-  // 23.6.8, comparison with T
-  template <class T, class U> constexpr bool operator==(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator==(const T&, const optional<U>&);
-  template <class T, class U> constexpr bool operator!=(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator!=(const T&, const optional<U>&);
-  template <class T, class U> constexpr bool operator<(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator<(const T&, const optional<U>&);
-  template <class T, class U> constexpr bool operator<=(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator<=(const T&, const optional<U>&);
-  template <class T, class U> constexpr bool operator>(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator>(const T&, const optional<U>&);
-  template <class T, class U> constexpr bool operator>=(const optional<T>&, const U&);
-  template <class T, class U> constexpr bool operator>=(const T&, const optional<U>&);
-
-  // 23.6.9, specialized algorithms
-  template <class T> void swap(optional<T>&, optional<T>&) noexcept(see below ); // constexpr in C++20
-  template <class T> constexpr optional<see below > make_optional(T&&);
-  template <class T, class... Args>
+    constexpr bool operator>=(const optional<T>&, const optional<U>&);
+  template<class T, three_way_comparable_with<T> U>
+    constexpr compare_three_way_result_t<T, U>
+      operator<=>(const optional<T>&, const optional<U>&); // since C++20
+
+  // [optional.nullops], comparison with nullopt
+  template<class T> constexpr bool operator==(const optional<T>&, nullopt_t) noexcept; // until C++17
+  template<class T> constexpr bool operator==(nullopt_t, const optional<T>&) noexcept; // until C++17
+  template<class T> constexpr bool operator!=(const optional<T>&, nullopt_t) noexcept; // until C++17
+  template<class T> constexpr bool operator!=(nullopt_t, const optional<T>&) noexcept; // until C++17
+  template<class T> constexpr bool operator<(const optional<T>&, nullopt_t) noexcept;  // until C++17
+  template<class T> constexpr bool operator<(nullopt_t, const optional<T>&) noexcept;  // until C++17
+  template<class T> constexpr bool operator<=(const optional<T>&, nullopt_t) noexcept; // until C++17
+  template<class T> constexpr bool operator<=(nullopt_t, const optional<T>&) noexcept; // until C++17
+  template<class T> constexpr bool operator>(const optional<T>&, nullopt_t) noexcept;  // until C++17
+  template<class T> constexpr bool operator>(nullopt_t, const optional<T>&) noexcept;  // until C++17
+  template<class T> constexpr bool operator>=(const optional<T>&, nullopt_t) noexcept; // until C++17
+  template<class T> constexpr bool operator>=(nullopt_t, const optional<T>&) noexcept; // until C++17
+  template<class T>
+    constexpr strong_ordering operator<=>(const optional<T>&, nullopt_t) noexcept;     // since C++20
+
+  // [optional.comp.with.t], comparison with T
+  template<class T, class U> constexpr bool operator==(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator==(const T&, const optional<U>&);
+  template<class T, class U> constexpr bool operator!=(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator!=(const T&, const optional<U>&);
+  template<class T, class U> constexpr bool operator<(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator<(const T&, const optional<U>&);
+  template<class T, class U> constexpr bool operator<=(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator<=(const T&, const optional<U>&);
+  template<class T, class U> constexpr bool operator>(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator>(const T&, const optional<U>&);
+  template<class T, class U> constexpr bool operator>=(const optional<T>&, const U&);
+  template<class T, class U> constexpr bool operator>=(const T&, const optional<U>&);
+  template<class T, class U>
+      requires (!is-derived-from-optional<U>) && three_way_comparable_with<T, U>
+    constexpr compare_three_way_result_t<T, U>
+      operator<=>(const optional<T>&, const U&);                                       // since C++20
+
+  // [optional.specalg], specialized algorithms
+  template<class T>
+    void swap(optional<T>&, optional<T>&) noexcept(see below ); // constexpr in C++20
+  
+  template<class T>
+    constexpr optional<see below > make_optional(T&&);
+  template<class T, class... Args>
     constexpr optional<T> make_optional(Args&&... args);
-  template <class T, class U, class... Args>
+  template<class T, class U, class... Args>
     constexpr optional<T> make_optional(initializer_list<U> il, Args&&... args);
 
-  // 23.6.10, hash support
-  template <class T> struct hash;
-  template <class T> struct hash<optional<T>>;
+  // [optional.hash], hash support
+  template<class T> struct hash;
+  template<class T> struct hash<optional<T>>;
 
-  template <class T> class optional {
+  template<class T>
+  class optional {
   public:
     using value_type = T;
 
-    // 23.6.3.1, constructors
+    // [optional.ctor], constructors
     constexpr optional() noexcept;
     constexpr optional(nullopt_t) noexcept;
     constexpr optional(const optional &);
     constexpr optional(optional &&) noexcept(see below);
-    template <class... Args> constexpr explicit optional(in_place_t, Args &&...);
-    template <class U, class... Args>
+    template<class... Args>
+      constexpr explicit optional(in_place_t, Args &&...);
+    template<class U, class... Args>
       constexpr explicit optional(in_place_t, initializer_list<U>, Args &&...);
-    template <class U = T>
+    template<class U = T>
       constexpr explicit(see-below) optional(U &&);
-    template <class U>
+    template<class U>
       explicit(see-below) optional(const optional<U> &);         // constexpr in C++20
-    template <class U>
+    template<class U>
       explicit(see-below) optional(optional<U> &&);              // constexpr in C++20
 
-    // 23.6.3.2, destructor
+    // [optional.dtor], destructor
     ~optional(); // constexpr in C++20
 
-    // 23.6.3.3, assignment
-    optional &operator=(nullopt_t) noexcept;                     // constexpr in C++20
+    // [optional.assign], assignment
+    optional &operator=(nullopt_t) noexcept;                        // constexpr in C++20
     constexpr optional &operator=(const optional &);
     constexpr optional &operator=(optional &&) noexcept(see below);
-    template <class U = T> optional &operator=(U &&);            // constexpr in C++20
-    template <class U> optional &operator=(const optional<U> &); // constexpr in C++20
-    template <class U> optional &operator=(optional<U> &&);      // constexpr in C++20
-    template <class... Args> T& emplace(Args &&...);             // constexpr in C++20
-    template <class U, class... Args>
-      T& emplace(initializer_list<U>, Args &&...);               // constexpr in C++20
-
-    // 23.6.3.4, swap
+    template<class U = T>
+      optional &operator=(U &&);                                    // constexpr in C++20
+    template<class U>
+      optional &operator=(const optional<U> &);                     // constexpr in C++20
+    template<class U>
+      optional &operator=(optional<U> &&);                          // constexpr in C++20
+    template<class... Args>
+      T& emplace(Args &&...);                                       // constexpr in C++20
+    template<class U, class... Args>
+      T& emplace(initializer_list<U>, Args &&...);                  // constexpr in C++20
+
+    // [optional.swap], swap
     void swap(optional &) noexcept(see below ); // constexpr in C++20
 
-    // 23.6.3.5, observers
+    // [optional.observe], observers
     constexpr T const *operator->() const;
     constexpr T *operator->();
     constexpr T const &operator*() const &;
@@ -129,8 +147,8 @@
     constexpr T &value() &;
     constexpr T &&value() &&;
     constexpr const T &&value() const &&;
-    template <class U> constexpr T value_or(U &&) const &;
-    template <class U> constexpr T value_or(U &&) &&;
+    template<class U> constexpr T value_or(U &&) const &;
+    template<class U> constexpr T value_or(U &&) &&;
 
     // [optional.monadic], monadic operations
     template<class F> constexpr auto and_then(F&& f) &;         // since C++23
@@ -144,15 +162,15 @@
     template<class F> constexpr optional or_else(F&& f) &&;     // since C++23
     template<class F> constexpr optional or_else(F&& f) const&; // since C++23
 
-    // 23.6.3.6, modifiers
+    // [optional.mod], modifiers
     void reset() noexcept; // constexpr in C++20
 
   private:
-    T *val; // exposition only
+    T *val;         // exposition only
   };
 
-template<class T>
-  optional(T) -> optional<T>;
+  template<class T>
+    optional(T) -> optional<T>;
 
 } // namespace std
 
@@ -160,6 +178,8 @@
 
 #include <__assert> // all public C++ headers provide the assertion handler
 #include <__availability>
+#include <__compare/compare_three_way_result.h>
+#include <__compare/three_way_comparable.h>
 #include <__concepts/invocable.h>
 #include <__config>
 #include <__functional/hash.h>
@@ -1288,6 +1308,20 @@
     return *__x >= *__y;
 }
 
+#if _LIBCPP_STD_VER >= 20
+
+template<class _Tp, three_way_comparable_with<_Tp> _Up>
+_LIBCPP_HIDE_FROM_ABI
+constexpr compare_three_way_result_t<_Tp, _Up>
+operator<=>(const optional<_Tp>& __x, const optional<_Up>& __y)
+{
+    if (__x && __y)
+        return *__x <=> *__y;
+    return __x.has_value() <=> __y.has_value();
+}
+
+#endif
+
 // Comparisons with nullopt
 template <class _Tp>
 _LIBCPP_INLINE_VISIBILITY constexpr
@@ -1297,6 +1331,8 @@
     return !static_cast<bool>(__x);
 }
 
+#if _LIBCPP_STD_VER <= 17
+
 template <class _Tp>
 _LIBCPP_INLINE_VISIBILITY constexpr
 bool
@@ -1385,6 +1421,18 @@
     return !static_cast<bool>(__x);
 }
 
+#elif _LIBCPP_STD_VER >= 20
+
+template<class _Tp>
+_LIBCPP_HIDE_FROM_ABI
+constexpr strong_ordering 
+operator<=>(const optional<_Tp>& __x, nullopt_t) noexcept
+{
+    return __x.has_value() <=> false;
+}
+
+#endif
+
 // Comparisons with T
 template <class _Tp, class _Up>
 _LIBCPP_INLINE_VISIBILITY constexpr
@@ -1530,6 +1578,19 @@
     return static_cast<bool>(__x) ? __v >= *__x : true;
 }
 
+#if _LIBCPP_STD_VER >= 20
+
+template<class _Tp, class _Up>
+    requires (!__is_std_optional<_Up>::value) && three_way_comparable_with<_Tp, _Up>
+_LIBCPP_HIDE_FROM_ABI
+constexpr compare_three_way_result_t<_Tp, _Up>
+operator<=>(const optional<_Tp>& __x, const _Up& __v)
+{
+    return __x.has_value() ? *__x <=> __v : strong_ordering::less;
+}
+
+#endif
+
 
 template <class _Tp>
 inline _LIBCPP_INLINE_VISIBILITY _LIBCPP_CONSTEXPR_SINCE_CXX20
diff --git a/libcxx/test/std/utilities/optional/optional.comp_with_t/compare.three_way.pass.cpp b/libcxx/test/std/utilities/optional/optional.comp_with_t/compare.three_way.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/utilities/optional/optional.comp_with_t/compare.three_way.pass.cpp
@@ -0,0 +1,54 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// <optional>
+
+// [optional.comp.with.t], comparison with T
+
+// template<class T, class U>
+//     requires (!is-derived-from-optional<U>) && three_way_comparable_with<T, U>
+//   constexpr compare_three_way_result_t<T, U>
+//     operator<=>(const optional<T>&, const U&);
+
+#include <cassert>
+#include <compare>
+#include <optional>
+
+#include "test_comparisons.h"
+
+constexpr bool test() {
+  // [optional.comp.with.t], comparison with T
+  {
+    int t{2};
+    std::optional<int> op{3};
+    assert((t <=> op) == std::strong_ordering::less);
+    assert(testOrder(t, op, std::strong_ordering::less));
+  }
+  {
+    int t{3};
+    std::optional<int> op{2};
+    assert((t <=> op) == std::strong_ordering::greater);
+    assert(testOrder(t, op, std::strong_ordering::greater));
+  }
+  {
+    int t{3};
+    std::optional<int> op{3};
+    assert((t <=> op) == std::strong_ordering::equal);
+    assert(testOrder(t, op, std::strong_ordering::equal));
+  }
+
+  return true;
+}
+
+int main() {
+  assert(test());
+  static_assert(test());
+  return 0;
+}
diff --git a/libcxx/test/std/utilities/optional/optional.nullops/compare.three_way.pass.cpp b/libcxx/test/std/utilities/optional/optional.nullops/compare.three_way.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/utilities/optional/optional.nullops/compare.three_way.pass.cpp
@@ -0,0 +1,51 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// <optional>
+
+// [optional.nullops], comparison with nullopt
+
+// template<class T>
+//   constexpr strong_ordering operator<=>(const optional<T>&, nullopt_t) noexcept;
+
+#include <cassert>
+#include <compare>
+#include <optional>
+
+#include "test_comparisons.h"
+
+constexpr bool test() {
+  // [optional.nullops], comparison with nullopt
+  {
+    std::optional<int> op{1};
+    assert((std::nullopt <=> op) == std::strong_ordering::less);
+    assert(testOrder(std::nullopt, op, std::strong_ordering::less));
+  }
+  {
+    std::optional<int> op{1};
+    assert((op <=> std::nullopt) == std::strong_ordering::greater);
+    assert(testOrder(op, std::nullopt, std::strong_ordering::greater));
+  }
+  {
+    std::optional<int> op;
+    assert((std::nullopt <=> op) == std::strong_ordering::equal);
+    assert(testOrder(std::nullopt, op, std::strong_ordering::equal));
+    assert((op <=> std::nullopt) == std::strong_ordering::equal);
+    assert(testOrder(op, std::nullopt, std::strong_ordering::equal));
+  }
+
+  return true;
+}
+
+int main() {
+  assert(test());
+  static_assert(test());
+  return 0;
+}
diff --git a/libcxx/test/std/utilities/optional/optional.relops/compare.three_way.pass.cpp b/libcxx/test/std/utilities/optional/optional.relops/compare.three_way.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/utilities/optional/optional.relops/compare.three_way.pass.cpp
@@ -0,0 +1,64 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// <optional>
+
+// [optional.relops], relational operators
+
+// template<class T, three_way_comparable_with<T> U>
+//   constexpr compare_three_way_result_t<T, U>
+//     operator<=>(const optional<T>&, const optional<U>&);
+
+#include <cassert>
+#include <compare>
+#include <optional>
+
+#include "test_comparisons.h"
+
+constexpr bool test() {
+  // [optional.relops], relational operators
+  std::optional<int> op;
+
+  {
+    std::optional<int> op1{2};
+    std::optional<int> op2{3};
+    assert((op <=> op2) == std::strong_ordering::less);
+    assert(testOrder(op, op2, std::strong_ordering::less));
+    assert((op1 <=> op2) == std::strong_ordering::less);
+    assert(testOrder(op1, op2, std::strong_ordering::less));
+  }
+  {
+    std::optional<int> op1{3};
+    std::optional<int> op2{2};
+    assert((op1 <=> op) == std::strong_ordering::greater);
+    assert(testOrder(op1, op, std::strong_ordering::greater));
+    assert((op1 <=> op2) == std::strong_ordering::greater);
+    assert(testOrder(op1, op2, std::strong_ordering::greater));
+  }
+  {
+    assert((op <=> op) == std::strong_ordering::equal);
+    assert(testOrder(op, op, std::strong_ordering::equal));
+
+    std::optional<int> op1{3};
+    std::optional<int> op2{3};
+    assert((op1 <=> op1) == std::strong_ordering::equal);
+    assert(testOrder(op1, op1, std::strong_ordering::equal));
+    assert((op1 <=> op2) == std::strong_ordering::equal);
+    assert(testOrder(op1, op2, std::strong_ordering::equal));
+  }
+
+  return true;
+}
+
+int main() {
+  assert(test());
+  static_assert(test());
+  return 0;
+}