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
@@ -186,16 +186,27 @@
         std::forward<Params>(params)...);
   }
 
+  template <typename Callable,
+            typename Result =
+                typename std::result_of<Callable(Params...)>::type>
+  static constexpr bool IsCompatible =
+      std::is_void<Ret>::value || std::is_convertible<Result, Ret>::value;
+
 public:
   function_ref() = default;
   function_ref(std::nullptr_t) {}
 
   template <typename Callable>
+  // Only allow this constructor if the object is actually callable
+  // and returns the correct type.
   function_ref(
       Callable &&callable,
       std::enable_if_t<
+          // This is not the copy-constructor.
           !std::is_same<std::remove_cv_t<std::remove_reference_t<Callable>>,
-                        function_ref>::value> * = nullptr)
+                        function_ref>::value &&
+          // Must be callable and return a suitable type.
+          IsCompatible<Callable>> * = nullptr)
       : callback(callback_fn<typename std::remove_reference<Callable>::type>),
         callable(reinterpret_cast<intptr_t>(&callable)) {}
 
diff --git a/llvm/lib/AsmParser/LLParser.h b/llvm/lib/AsmParser/LLParser.h
--- a/llvm/lib/AsmParser/LLParser.h
+++ b/llvm/lib/AsmParser/LLParser.h
@@ -166,8 +166,8 @@
         : Context(Context), Lex(F, SM, Err, Context), M(M), Index(Index),
           Slots(Slots), BlockAddressPFS(nullptr) {}
     bool Run(
-        bool UpgradeDebugInfo,
-        DataLayoutCallbackTy DataLayoutCallback = [](Module *) {});
+        bool UpgradeDebugInfo, DataLayoutCallbackTy DataLayoutCallback =
+                                   [](StringRef) { return None; });
 
     bool parseStandaloneConstantValue(Constant *&C, const SlotMapping *Slots);
 
diff --git a/llvm/lib/Bitcode/Reader/BitcodeReader.cpp b/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
--- a/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
+++ b/llvm/lib/Bitcode/Reader/BitcodeReader.cpp
@@ -579,9 +579,7 @@
   /// \returns true if an error occurred.
   Error parseBitcodeInto(
       Module *M, bool ShouldLazyLoadMetadata = false, bool IsImporting = false,
-      DataLayoutCallbackTy DataLayoutCallback = [](std::string) {
-        return None;
-      });
+      DataLayoutCallbackTy DataLayoutCallback = [](StringRef) { return None; });
 
   static uint64_t decodeSignRotatedValue(uint64_t V);
 
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