diff --git a/google/cloud/functions/framework.h b/google/cloud/functions/framework.h
index 438a7c8e..bc795191 100644
--- a/google/cloud/functions/framework.h
+++ b/google/cloud/functions/framework.h
@@ -15,6 +15,7 @@
 #ifndef FUNCTIONS_FRAMEWORK_CPP_GOOGLE_CLOUD_FUNCTIONS_FRAMEWORK_H
 #define FUNCTIONS_FRAMEWORK_CPP_GOOGLE_CLOUD_FUNCTIONS_FRAMEWORK_H
 
+#include "google/cloud/functions/function.h"
 #include "google/cloud/functions/user_functions.h"
 #include "google/cloud/functions/version.h"
 #include <functional>
@@ -22,13 +23,51 @@
 namespace google::cloud::functions {
 FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_BEGIN
 
+/**
+ * Runs function wrapped by @p handler.
+ *
+ * Starts a HTTP server at the address and listening endpoint described by
+ * @p argv, invoking @p handler to handle any HTTP request.
+ *
+ * If @p handler wraps a function with the Cloud Event signature, then the
+ * incoming HTTP requests **MUST** conform to the Cloud Events [HTTP protocol
+ * binding specification][cloud-events-spec].
+ *
+ * @note
+ * When deploying code to Google Cloud Functions applications should **not** use
+ * this function directly. The buildpack will automatically create a `main()`
+ * and invoke `Run()` with the correct parameters. We recommend that application
+ * developers use this function only for local development and integration
+ * tests.
+ *
+ * @par Example
+ * @code
+ * namespace gcf = ::google::cloud::functions;
+ *
+ * extern gcf::HttpResponse MyHandler(gcf::HttpRequest);
+ *
+ * int main(int argc, char* argv[]) {
+ *   return gcf::Run(argc, argv, gcf::MakeFunction(MyHandler));
+ * }
+ * @endcode
+ *
+ * @see ParseOptions for more details of the command-line arguments used by this
+ *     function.
+ *
+ * [cloud-events-spec]:
+ * https://github.com/cloudevents/spec/blob/v1.0/http-protocol-binding.md
+ */
+int Run(int argc, char const* const argv[], Function const& handler) noexcept;
+
 /**
  * Run the given function, invoking it to handle HTTP requests.
  *
+ * @deprecated Prefer using the overload consuming a `Function` object.
+ *
  * Starts a HTTP server at the address and listening endpoint described by
  * @p argv, invoking @p handler to handle any HTTP request.
  *
- * When deploying code to Google Cloud Functions applications should**not** use
+ * When deploying code to Google Cloud Functions applications should **not** use
  * this function directly. The buildpack will automatically create a `main()`
  * and invoke `Run()` with the correct parameters. We recommend that application
  * developers use this function only for local development and integration
@@ -53,11 +92,13 @@ int Run(int argc, char const* const argv[], UserHttpFunction handler) noexcept;
 /**
  * Run the given function, invoking it to handle Cloud Events.
  *
+ * @deprecated Prefer using the overload consuming a `Function` object.
+ *
  * Starts a HTTP server at the address and listening endpoint described by
  * @p argv, invoking @p handler to handle any HTTP request which *MUST* conform
  * to the Cloud Events [HTTP protocol binding][cloud-events-spec].
  *
- * When deploying code to Google Cloud Functions applications should**not** use
+ * When deploying code to Google Cloud Functions applications should **not** use
  * this function directly. The buildpack will automatically create a `main()`
  * and invoke `Run()` with the correct parameters. We recommend that application
  * developers use this function only for local development and integration
diff --git a/google/cloud/functions/integration_tests/cloud_event_conformance.cc b/google/cloud/functions/integration_tests/cloud_event_conformance.cc
index ee9e9472..66d04510 100644
--- a/google/cloud/functions/integration_tests/cloud_event_conformance.cc
+++ b/google/cloud/functions/integration_tests/cloud_event_conformance.cc
@@ -63,6 +63,6 @@ void CloudEventConformance(functions::CloudEvent const& ev) {
 
 int main(int argc, char* argv[]) {
   return google::cloud::functions_internal::RunForTest(
-      argc, argv, CloudEventConformance, [] { return shutdown_server.load(); },
-      [](int /*port*/) {});
+      argc, argv, functions::MakeFunction(CloudEventConformance),
+      [] { return shutdown_server.load(); }, [](int /*port*/) {});
 }
diff --git a/google/cloud/functions/integration_tests/cloud_event_handler.cc b/google/cloud/functions/integration_tests/cloud_event_handler.cc
index 9d0a18ab..48370a64 100644
--- a/google/cloud/functions/integration_tests/cloud_event_handler.cc
+++ b/google/cloud/functions/integration_tests/cloud_event_handler.cc
@@ -38,6 +38,6 @@ void CloudEventHandler(CloudEvent const& event) {
 
 int main(int argc, char* argv[]) {
   return google::cloud::functions_internal::RunForTest(
-      argc, argv, CloudEventHandler, [] { return shutdown_server.load(); },
-      [](int /*port*/) {});
+      argc, argv, google::cloud::functions::MakeFunction(CloudEventHandler),
+      [] { return shutdown_server.load(); }, [](int /*port*/) {});
 }
diff --git a/google/cloud/functions/integration_tests/echo_server.cc b/google/cloud/functions/integration_tests/echo_server.cc
index 09389232..e5eff03d 100644
--- a/google/cloud/functions/integration_tests/echo_server.cc
+++ b/google/cloud/functions/integration_tests/echo_server.cc
@@ -71,6 +71,6 @@ HttpResponse EchoServer(HttpRequest const& request) {
 
 int main(int argc, char* argv[]) {
   return google::cloud::functions_internal::RunForTest(
-      argc, argv, EchoServer, [] { return shutdown_server.load(); },
-      [](int /*port*/) {});
+      argc, argv, google::cloud::functions::MakeFunction(EchoServer),
+      [] { return shutdown_server.load(); }, [](int /*port*/) {});
 }
diff --git a/google/cloud/functions/integration_tests/http_conformance.cc b/google/cloud/functions/integration_tests/http_conformance.cc
index 2694d53e..33e6c3bd 100644
--- a/google/cloud/functions/integration_tests/http_conformance.cc
+++ b/google/cloud/functions/integration_tests/http_conformance.cc
@@ -30,6 +30,6 @@ functions::HttpResponse HttpConformance(functions::HttpRequest const& request) {
 
 int main(int argc, char* argv[]) {
   return google::cloud::functions_internal::RunForTest(
-      argc, argv, HttpConformance, [] { return shutdown_server.load(); },
-      [](int /*port*/) {});
+      argc, argv, google::cloud::functions::MakeFunction(HttpConformance),
+      [] { return shutdown_server.load(); }, [](int /*port*/) {});
 }
diff --git a/google/cloud/functions/internal/framework_impl.cc b/google/cloud/functions/internal/framework_impl.cc
index e53f5a3b..4a4a43d9 100644
--- a/google/cloud/functions/internal/framework_impl.cc
+++ b/google/cloud/functions/internal/framework_impl.cc
@@ -13,7 +13,7 @@
 // limitations under the License.
 
 #include "google/cloud/functions/internal/framework_impl.h"
-#include "google/cloud/functions/internal/call_user_function.h"
+#include "google/cloud/functions/internal/function_impl.h"
 #include "google/cloud/functions/internal/parse_options.h"
 #include "google/cloud/functions/version.h"
 #include <boost/asio/ip/tcp.hpp>
@@ -34,12 +34,12 @@ namespace be = boost::beast;
 namespace asio = boost::asio;
 using tcp = boost::asio::ip::tcp;
 
-template <typename UserFunction>
-void HandleSession(tcp::socket socket, UserFunction const& user_function) {
+void HandleSession(tcp::socket socket, Handler const& handler) {
   auto report_error = [](be::error_code ec, char const* what) {
     // TODO(#35) - maybe replace with Boost.Log
     std::cerr << what << ": " << ec.message() << "\n";
   };
+
   be::error_code ec;
   for (;;) {
     be::flat_buffer buffer;
@@ -49,7 +49,7 @@ void HandleSession(tcp::socket socket, UserFunction const& user_function) {
     if (ec == be::http::error::end_of_stream) break;
     if (ec) return report_error(ec, "read");
     auto const keep_alive = request.keep_alive();
-    auto response = CallUserFunction(user_function, std::move(request));
+    auto response = handler(std::move(request));
     // Flush any buffered output, as the application may be shutdown immediately
     // after the HTTP response is sent.
     std::cout << std::flush;
@@ -65,8 +65,8 @@ void HandleSession(tcp::socket socket, UserFunction const& user_function) {
   socket.shutdown(tcp::socket::shutdown_send, ec);
 }
 
-template <typename UserFunction>
-int RunForTestImpl(int argc, char const* const argv[], UserFunction&& function,
+int RunForTestImpl(int argc, char const* const argv[],
+                   functions::Function const& function,
                    std::function<bool()> const& shutdown,
                    std::function<void(int)> const& actual_port) {
   auto vm = ParseOptions(argc, argv);
@@ -74,16 +74,18 @@ int RunForTestImpl(int argc, char const* const argv[], UserFunction&& function,
 
   auto address = asio::ip::make_address(vm["address"].as<std::string>());
   auto port = vm["port"].as<int>();
+  auto target = vm["target"].as<std::string>();
 
   asio::io_context ioc{1};
   tcp::acceptor acceptor{ioc, {address, static_cast<std::uint16_t>(port)}};
   acceptor.listen(boost::asio::socket_base::max_connections);
   actual_port(acceptor.local_endpoint().port());
 
-  auto handle_session =
-      [h = std::forward<UserFunction>(function)](tcp::socket socket) {
-        HandleSession(std::move(socket), h);
-      };
+  auto handler = FunctionImpl::GetImpl(function)->GetHandler(target);
+
+  auto handle_session = [h = std::move(handler)](tcp::socket socket) {
+    HandleSession(std::move(socket), h);
+  };
 
   auto cleanup = [](std::vector<std::future<void>> sessions, auto wait) {
     std::vector<std::future<void>> running;
@@ -124,11 +126,10 @@ int RunForTestImpl(int argc, char const* const argv[], UserFunction&& function,
   return 0;
 }
 
-template <typename UserFunction>
-int RunImpl(int argc, char const* const argv[], UserFunction&& f) noexcept try {
+int RunImpl(int argc, char const* const argv[],
+            functions::Function const& f) noexcept try {
   return RunForTestImpl(
-      argc, argv, std::forward<UserFunction>(f), [] { return false; },
-      [](int /*unused*/) {});
+      argc, argv, f, [] { return false; }, [](int /*unused*/) {});
 } catch (std::exception const& ex) {
   std::cerr << "Standard C++ exception thrown " << ex.what() << "\n";
   return 1;
@@ -140,17 +141,10 @@ int RunImpl(int argc, char const* const argv[], UserFunction&& f) noexcept try {
 }  // namespace
 
 int RunForTest(int argc, char const* const argv[],
-               functions::UserHttpFunction handler,
-               std::function<bool()> const& shutdown,
-               std::function<void(int)> const& actual_port) {
-  return RunForTestImpl(argc, argv, std::move(handler), shutdown, actual_port);
-}
-
-int RunForTest(int argc, char const* const argv[],
-               functions::UserCloudEventFunction handler,
+               functions::Function const& handler,
                std::function<bool()> const& shutdown,
                std::function<void(int)> const& actual_port) {
-  return RunForTestImpl(argc, argv, std::move(handler), shutdown, actual_port);
+  return RunForTestImpl(argc, argv, handler, shutdown, actual_port);
 }
 
 FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_END
@@ -159,13 +153,19 @@ FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_END
 namespace google::cloud::functions {
 FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_BEGIN
 
+int Run(int argc, char const* const argv[], Function const& handler) noexcept {
+  return functions_internal::RunImpl(argc, argv, handler);
+}
+
 int Run(int argc, char const* const argv[], UserHttpFunction handler) noexcept {
-  return functions_internal::RunImpl(argc, argv, std::move(handler));
+  return functions_internal::RunImpl(
+      argc, argv, functions::MakeFunction(std::move(handler)));
 }
 
 int Run(int argc, char const* const argv[],
         UserCloudEventFunction handler) noexcept {
-  return functions_internal::RunImpl(argc, argv, std::move(handler));
+  return functions_internal::RunImpl(
+      argc, argv, functions::MakeFunction(std::move(handler)));
 }
 
 FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_END
diff --git a/google/cloud/functions/internal/framework_impl.h b/google/cloud/functions/internal/framework_impl.h
index 0a7f6f3d..70b2be67 100644
--- a/google/cloud/functions/internal/framework_impl.h
+++ b/google/cloud/functions/internal/framework_impl.h
@@ -15,6 +15,7 @@
 #ifndef FUNCTIONS_FRAMEWORK_CPP_GOOGLE_CLOUD_FUNCTIONS_INTERNAL_FRAMEWORK_IMPL_H
 #define FUNCTIONS_FRAMEWORK_CPP_GOOGLE_CLOUD_FUNCTIONS_INTERNAL_FRAMEWORK_IMPL_H
 
+#include "google/cloud/functions/function.h"
 #include "google/cloud/functions/user_functions.h"
 #include "google/cloud/functions/version.h"
 #include <functional>
@@ -24,13 +25,7 @@ FUNCTIONS_FRAMEWORK_CPP_INLINE_NAMESPACE_BEGIN
 
 /// Implement functions::Run(), with additional helpers for testing.
 int RunForTest(int argc, char const* const argv[],
-               functions::UserHttpFunction handler,
-               std::function<bool()> const& shutdown,
-               std::function<void(int)> const& actual_port);
-
-/// Implement functions::Run(), with additional helpers for testing.
-int RunForTest(int argc, char const* const argv[],
-               functions::UserCloudEventFunction handler,
+               functions::Function const& handler,
                std::function<bool()> const& shutdown,
                std::function<void(int)> const& actual_port);
 
diff --git a/google/cloud/functions/internal/framework_impl_test.cc b/google/cloud/functions/internal/framework_impl_test.cc
index 63ec7e35..b2adf745 100644
--- a/google/cloud/functions/internal/framework_impl_test.cc
+++ b/google/cloud/functions/internal/framework_impl_test.cc
@@ -110,7 +110,8 @@ TEST(FrameworkTest, Http) {
   auto run = [&](int argc, char const* const argv[],
                  functions::UserHttpFunction f) {
     return RunForTest(
-        argc, argv, std::move(f), [&shutdown]() { return shutdown.load(); },
+        argc, argv, functions::MakeFunction(std::move(f)),
+        [&shutdown]() { return shutdown.load(); },
         [&port_p](int port) mutable { port_p.set_value(port); });
   };
   auto done = std::async(std::launch::async, run, static_cast<int>(kTestArgc),
@@ -143,7 +144,8 @@ TEST(FrameworkTest, CloudEvent) {
   auto run = [&](int argc, char const* const argv[],
                  functions::UserCloudEventFunction f) {
     return RunForTest(
-        argc, argv, std::move(f), [&shutdown]() { return shutdown.load(); },
+        argc, argv, functions::MakeFunction(std::move(f)),
+        [&shutdown]() { return shutdown.load(); },
         [&port_p](int port) mutable { port_p.set_value(port); });
   };
   auto done = std::async(std::launch::async, run, static_cast<int>(kTestArgc),