diff --git a/llvm/include/llvm/ADT/STLExtras.h b/llvm/include/llvm/ADT/STLExtras.h
--- a/llvm/include/llvm/ADT/STLExtras.h
+++ b/llvm/include/llvm/ADT/STLExtras.h
@@ -190,9 +190,17 @@
   function_ref() = default;
   function_ref(std::nullptr_t) {}
 
-  template <typename Callable>
+  template <typename Callable,
+            // Only allow this constructor if the object is actually callable
+            // and returns the correct type.
+            typename = typename std::enable_if<
+                std::is_void<Ret>::value ||
+                std::is_convertible<
+                    typename std::result_of<Callable(Params...)>::type,
+                    Ret>::value>::type>
   function_ref(
       Callable &&callable,
+      // This is not a copy-constructor.
       std::enable_if_t<
           !std::is_same<std::remove_cv_t<std::remove_reference_t<Callable>>,
                         function_ref>::value> * = nullptr)
diff --git a/llvm/unittests/ADT/FunctionRefTest.cpp b/llvm/unittests/ADT/FunctionRefTest.cpp
--- a/llvm/unittests/ADT/FunctionRefTest.cpp
+++ b/llvm/unittests/ADT/FunctionRefTest.cpp
@@ -48,4 +48,15 @@
   ASSERT_EQ(1, X());
 }
 
+// Test that overloads on function_refs are resolved as expected.
+const char *returns(StringRef) { return "not a function"; }
+const char *returns(function_ref<double()> F) { return "number"; }
+const char *returns(function_ref<StringRef()> F) { return "string"; }
+
+TEST(FunctionRefTest, SFINAE) {
+  EXPECT_EQ("not a function", returns("boo!"));
+  EXPECT_EQ("number", returns([] { return 42; }));
+  EXPECT_EQ("string", returns([] { return "hello"; }));
+}
+
 } // namespace