diff --git a/libcxx/include/type_traits b/libcxx/include/type_traits
--- a/libcxx/include/type_traits
+++ b/libcxx/include/type_traits
@@ -3491,10 +3491,36 @@
     -> decltype(      static_cast<_Fp&&>(__f)(static_cast<_Args&&>(__args)...))
     { return          static_cast<_Fp&&>(__f)(static_cast<_Args&&>(__args)...); }
 
-// __invokable
-template <class _Ret, class _Fp, class ..._Args>
-struct __invokable_r
-{
+// __invokable_r
+
+// Detects whether an express of type _From can be implicitly converted to _To
+// according to [conv]. Note that this is distinct from is_convertible, which
+// for non-reference _From types relies on returning an rvalue reference from a
+// function and therefore gives the wrong answer for non-moveable types.
+//
+// REQUIRES: _From is not cv void.
+template <class _From, class _To>
+struct __is_implicitly_convertible {
+private:
+  template <class _Tp>
+  static void _RequireImplicitlyConvertibleTo(_Tp);
+
+  template <class _Tp>
+  static _Tp _Make();
+
+  template <class _Tp, class = decltype(_RequireImplicitlyConvertibleTo<_To>(_Make<_Tp>()))>
+  static true_type _TestImplicitConversion(int);
+
+  template <class _Tp>
+  static false_type _TestImplicitConversion(...);
+
+public:
+  using type = decltype(_TestImplicitConversion<_From>(0));
+  static constexpr bool value = type::value;
+};
+
+template <class _Ret, class _Fp, class... _Args>
+struct __invokable_r {
   template <class _XFp, class ..._XArgs>
   static auto __try_call(int) -> decltype(
     _VSTD::__invoke(declval<_XFp>(), declval<_XArgs>()...));
@@ -3511,12 +3537,14 @@
       typename conditional<
           is_void<_Ret>::value,
           true_type,
-          is_convertible<_Result, _Ret>
+          __is_implicitly_convertible<_Result, _Ret>
       >::type,
       false_type
   >::type;
   static const bool value = type::value;
 };
+
+// __invokable
 template <class _Fp, class ..._Args>
 using __invokable = __invokable_r<void, _Fp, _Args...>;
 
diff --git a/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r.compile.pass.cpp b/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r.compile.pass.cpp
@@ -0,0 +1,103 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// is_invocable_r
+
+#include <type_traits>
+
+// Non-invocable types
+
+static_assert(!std::is_invocable_r<void, void>::value);
+static_assert(!std::is_invocable_r<void, int>::value);
+static_assert(!std::is_invocable_r<void, int*>::value);
+static_assert(!std::is_invocable_r<void, int&>::value);
+static_assert(!std::is_invocable_r<void, int&&>::value);
+
+// Result type matches
+
+template <typename T>
+T Return();
+
+static_assert(std::is_invocable_r<int, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<char, decltype(Return<char>)>::value);
+static_assert(std::is_invocable_r<int*, decltype(Return<int*>)>::value);
+static_assert(std::is_invocable_r<int&, decltype(Return<int&>)>::value);
+static_assert(std::is_invocable_r<int&&, decltype(Return<int&&>)>::value);
+
+// void result type
+
+// Any actual return type should be useable with a result type of void.
+static_assert(std::is_invocable_r<void, decltype(Return<void>)>::value);
+static_assert(std::is_invocable_r<void, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<void, decltype(Return<int*>)>::value);
+static_assert(std::is_invocable_r<void, decltype(Return<int&>)>::value);
+static_assert(std::is_invocable_r<void, decltype(Return<int&&>)>::value);
+
+// const- and volatile-qualified void should work too.
+static_assert(std::is_invocable_r<const void, decltype(Return<void>)>::value);
+static_assert(std::is_invocable_r<const void, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<volatile void, decltype(Return<void>)>::value);
+static_assert(std::is_invocable_r<volatile void, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<const volatile void, decltype(Return<void>)>::value);
+static_assert(std::is_invocable_r<const volatile void, decltype(Return<int>)>::value);
+
+// Conversion of result type
+
+// It should be possible to use a result type to which the actual return type
+// can be converted.
+static_assert(std::is_invocable_r<char, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<const int*, decltype(Return<int*>)>::value);
+static_assert(std::is_invocable_r<void*, decltype(Return<int*>)>::value);
+static_assert(std::is_invocable_r<const int&, decltype(Return<int>)>::value);
+static_assert(std::is_invocable_r<const int&, decltype(Return<int&>)>::value);
+static_assert(std::is_invocable_r<const int&, decltype(Return<int&&>)>::value);
+static_assert(std::is_invocable_r<const char&, decltype(Return<int>)>::value);
+
+// But not a result type where the conversion doesn't work.
+static_assert(!std::is_invocable_r<int, decltype(Return<void>)>::value);
+static_assert(!std::is_invocable_r<int, decltype(Return<int*>)>::value);
+
+// Non-moveable result type
+
+// Define a type that can't be move-constructed.
+struct CantMove {
+  CantMove() = default;
+  CantMove(CantMove&&) = delete;
+};
+
+static_assert(!std::is_move_constructible_v<CantMove>);
+static_assert(!std::is_copy_constructible_v<CantMove>);
+
+// Define functions that return that type.
+CantMove MakeCantMove() { return {}; }
+CantMove MakeCantMoveWithArg(int) { return {}; }
+
+// Assumption check: it should be possible to call one of those functions and
+// use it to initialize a CantMove object.
+CantMove cant_move = MakeCantMove();
+
+// Therefore std::is_invocable_r should agree that they can be invoked to yield
+// a CantMove.
+static_assert(std::is_invocable_r<CantMove, decltype(MakeCantMove)>::value);
+static_assert(std::is_invocable_r<CantMove, decltype(MakeCantMoveWithArg), int>::value);
+
+// Of course it still shouldn't be possible to call one of the functions and get
+// back some other type.
+static_assert(!std::is_invocable_r<int, decltype(MakeCantMove)>::value);
+
+// And the argument types should still be important.
+static_assert(!std::is_invocable_r<CantMove, decltype(MakeCantMove), int>::value);
+static_assert(!std::is_invocable_r<CantMove, decltype(MakeCantMoveWithArg)>::value);
+
+// is_invocable_r
+
+// The struct form should be available too, not just the _v variant.
+static_assert(std::is_invocable_r<int, decltype(Return<int>)>::value);
+static_assert(!std::is_invocable_r<int*, decltype(Return<int>)>::value);
diff --git a/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r_v.compile.pass.cpp b/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r_v.compile.pass.cpp
new file mode 100644
--- /dev/null
+++ b/libcxx/test/std/utilities/meta/meta.rel/is_invocable_r_v.compile.pass.cpp
@@ -0,0 +1,103 @@
+//===----------------------------------------------------------------------===//
+//
+// 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
+
+// is_invocable_r
+
+#include <type_traits>
+
+// Non-invocable types
+
+static_assert(!std::is_invocable_r_v<void, void>);
+static_assert(!std::is_invocable_r_v<void, int>);
+static_assert(!std::is_invocable_r_v<void, int*>);
+static_assert(!std::is_invocable_r_v<void, int&>);
+static_assert(!std::is_invocable_r_v<void, int&&>);
+
+// Result type matches
+
+template <typename T>
+T Return();
+
+static_assert(std::is_invocable_r_v<int, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<char, decltype(Return<char>)>);
+static_assert(std::is_invocable_r_v<int*, decltype(Return<int*>)>);
+static_assert(std::is_invocable_r_v<int&, decltype(Return<int&>)>);
+static_assert(std::is_invocable_r_v<int&&, decltype(Return<int&&>)>);
+
+// void result type
+
+// Any actual return type should be useable with a result type of void.
+static_assert(std::is_invocable_r_v<void, decltype(Return<void>)>);
+static_assert(std::is_invocable_r_v<void, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<void, decltype(Return<int*>)>);
+static_assert(std::is_invocable_r_v<void, decltype(Return<int&>)>);
+static_assert(std::is_invocable_r_v<void, decltype(Return<int&&>)>);
+
+// const- and volatile-qualified void should work too.
+static_assert(std::is_invocable_r_v<const void, decltype(Return<void>)>);
+static_assert(std::is_invocable_r_v<const void, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<volatile void, decltype(Return<void>)>);
+static_assert(std::is_invocable_r_v<volatile void, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<const volatile void, decltype(Return<void>)>);
+static_assert(std::is_invocable_r_v<const volatile void, decltype(Return<int>)>);
+
+// Conversion of result type
+
+// It should be possible to use a result type to which the actual return type
+// can be converted.
+static_assert(std::is_invocable_r_v<char, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<const int*, decltype(Return<int*>)>);
+static_assert(std::is_invocable_r_v<void*, decltype(Return<int*>)>);
+static_assert(std::is_invocable_r_v<const int&, decltype(Return<int>)>);
+static_assert(std::is_invocable_r_v<const int&, decltype(Return<int&>)>);
+static_assert(std::is_invocable_r_v<const int&, decltype(Return<int&&>)>);
+static_assert(std::is_invocable_r_v<const char&, decltype(Return<int>)>);
+
+// But not a result type where the conversion doesn't work.
+static_assert(!std::is_invocable_r_v<int, decltype(Return<void>)>);
+static_assert(!std::is_invocable_r_v<int, decltype(Return<int*>)>);
+
+// Non-moveable result type
+
+// Define a type that can't be move-constructed.
+struct CantMove {
+  CantMove() = default;
+  CantMove(CantMove&&) = delete;
+};
+
+static_assert(!std::is_move_constructible_v<CantMove>);
+static_assert(!std::is_copy_constructible_v<CantMove>);
+
+// Define functions that return that type.
+CantMove MakeCantMove() { return {}; }
+CantMove MakeCantMoveWithArg(int) { return {}; }
+
+// Assumption check: it should be possible to call one of those functions and
+// use it to initialize a CantMove object.
+CantMove cant_move = MakeCantMove();
+
+// Therefore std::is_invocable_r should agree that they can be invoked to yield
+// a CantMove.
+static_assert(std::is_invocable_r_v<CantMove, decltype(MakeCantMove)>);
+static_assert(std::is_invocable_r_v<CantMove, decltype(MakeCantMoveWithArg), int>);
+
+// Of course it still shouldn't be possible to call one of the functions and get
+// back some other type.
+static_assert(!std::is_invocable_r_v<int, decltype(MakeCantMove)>);
+
+// And the argument types should still be important.
+static_assert(!std::is_invocable_r_v<CantMove, decltype(MakeCantMove), int>);
+static_assert(!std::is_invocable_r_v<CantMove, decltype(MakeCantMoveWithArg)>);
+
+// is_invocable_r
+
+// The struct form should be available too, not just the _v variant.
+static_assert(std::is_invocable_r<int, decltype(Return<int>)>::value);
+static_assert(!std::is_invocable_r<int*, decltype(Return<int>)>::value);
diff --git a/libcxx/test/std/utilities/meta/meta.rel/is_nothrow_invocable.pass.cpp b/libcxx/test/std/utilities/meta/meta.rel/is_nothrow_invocable.pass.cpp
--- a/libcxx/test/std/utilities/meta/meta.rel/is_nothrow_invocable.pass.cpp
+++ b/libcxx/test/std/utilities/meta/meta.rel/is_nothrow_invocable.pass.cpp
@@ -185,6 +185,21 @@
     static_assert(std::is_nothrow_invocable_r<Implicit, Fn, Tag&>::value, "");
     static_assert(throws_invocable_r<ThrowsImplicit, Fn, Tag&>(), "");
   }
+  {
+    // Check that it's fine if the result type is non-moveable.
+    struct CantMove {
+      CantMove() = default;
+      CantMove(CantMove&&) = delete;
+    };
+
+    static_assert(!std::is_move_constructible_v<CantMove>);
+    static_assert(!std::is_copy_constructible_v<CantMove>);
+
+    using Fn = CantMove() noexcept;
+
+    static_assert(std::is_nothrow_invocable_r<CantMove, Fn>::value);
+    static_assert(!std::is_nothrow_invocable_r<CantMove, Fn, int>::value);
+  }
   {
     // Check for is_nothrow_invocable_v
     using Fn = CallObject<true, int>;