diff --git a/thrust/testing/transform_iterator.cu b/thrust/testing/transform_iterator.cu
index 7bb87d4625..346f0fa8b5 100644
--- a/thrust/testing/transform_iterator.cu
+++ b/thrust/testing/transform_iterator.cu
@@ -6,6 +6,7 @@
 #include <thrust/sequence.h>
 
 #include <memory>
+#include <vector>
 
 #include <unittest/unittest.h>
 
@@ -108,3 +109,110 @@ void TestTransformIteratorNonCopyable()
 }
 
 DECLARE_UNITTEST(TestTransformIteratorNonCopyable);
+
+struct flip_value
+{
+  _CCCL_HOST_DEVICE bool operator()(bool b) const
+  {
+    return !b;
+  }
+};
+
+struct pass_ref
+{
+  _CCCL_HOST_DEVICE const bool& operator()(const bool& b) const
+  {
+    return b;
+  }
+};
+
+// TODO(bgruber): replace by libc++ with C++14
+struct forward
+{
+  template <class _Tp>
+  constexpr _Tp&& operator()(_Tp&& __t) const noexcept
+  {
+    return _CUDA_VSTD::forward<_Tp>(__t);
+  }
+};
+
+void TestTransformIteratorReferenceAndValueType()
+{
+  using ::cuda::std::is_same;
+  using ::cuda::std::negate;
+  {
+    thrust::host_vector<bool> v;
+    auto it = v.begin();
+    static_assert(is_same<decltype(*it), bool&>::value, "");
+    auto it_tr_val = thrust::make_transform_iterator(it, flip_value{});
+    static_assert(is_same<decltype(*it_tr_val), bool>::value, "");
+    auto it_tr_ref = thrust::make_transform_iterator(it, pass_ref{});
+    static_assert(is_same<decltype(*it_tr_ref), const bool&>::value, "");
+    auto it_tr_fwd = thrust::make_transform_iterator(it, forward{});
+  }
+
+  {
+    thrust::device_vector<bool> v;
+    auto it = v.begin();
+    static_assert(is_same<decltype(*it), thrust::device_reference<bool>>::value, "");
+    auto it_tr_val = thrust::make_transform_iterator(it, flip_value{});
+    static_assert(is_same<decltype(*it_tr_val), bool>::value, "");
+    auto it_tr_ref = thrust::make_transform_iterator(it, pass_ref{});
+    static_assert(is_same<decltype(*it_tr_ref), const bool&>::value, "");
+    auto it_tr_fwd = thrust::make_transform_iterator(it, forward{});
+    static_assert(is_same<decltype(*it_tr_fwd), const bool&>::value, ""); // device ref. is decayed
+  }
+
+  {
+    std::vector<bool> v;
+    auto it = v.begin();
+    static_assert(is_same<decltype(*it), std::vector<bool>::reference>::value, "");
+    auto it_tr_val = thrust::make_transform_iterator(it, flip_value{});
+    static_assert(is_same<decltype(*it_tr_val), bool>::value, "");
+    auto it_tr_ref = thrust::make_transform_iterator(it, pass_ref{});
+    static_assert(is_same<decltype(*it_tr_ref), const bool&>::value, "");
+    auto it_tr_fwd = thrust::make_transform_iterator(it, forward{});
+    static_assert(is_same<decltype(*it_tr_fwd), std::vector<bool>::reference&&>::value, ""); // No handling for std
+  }
+}
+DECLARE_UNITTEST(TestTransformIteratorReferenceAndValueType);
+
+struct foo
+{
+  int x, y;
+};
+
+struct access_x
+{
+  _CCCL_HOST_DEVICE int& operator()(foo& f) const noexcept
+  {
+    return f.x;
+  }
+};
+
+template <template <typename...> class SrcVec, template <typename...> class DstVec = SrcVec>
+void TestTransformIteratorAsDestinationWith()
+{
+  constexpr auto n = 10;
+  SrcVec<int> src(n, 1234);
+  DstVec<foo> dst(n, foo{1, 2});
+
+  thrust::copy(src.begin(), src.end(), thrust::make_transform_iterator(dst.begin(), access_x{}));
+
+  const thrust::host_vector<foo>& dst_h = dst; // no copy when Vec is a host vector
+  for (const auto& f : dst_h)
+  {
+    ASSERT_EQUAL(f.x, 1234);
+    ASSERT_EQUAL(f.y, 2);
+  }
+}
+
+void TestTransformIteratorAsDestination()
+{
+  TestTransformIteratorAsDestinationWith<thrust::host_vector>();
+  TestTransformIteratorAsDestinationWith<thrust::device_vector>();
+
+  TestTransformIteratorAsDestinationWith<thrust::host_vector, thrust::device_vector>();
+  TestTransformIteratorAsDestinationWith<thrust::device_vector, thrust::host_vector>();
+}
+DECLARE_UNITTEST(TestTransformIteratorAsDestination);
diff --git a/thrust/thrust/detail/reference.h b/thrust/thrust/detail/reference.h
index c96649f74e..88fdf3d87d 100644
--- a/thrust/thrust/detail/reference.h
+++ b/thrust/thrust/detail/reference.h
@@ -308,7 +308,7 @@ class reference
   pointer const ptr;
 
   // `thrust::detail::is_wrapped_reference` is a trait that indicates whether
-  // a type is a fancy reference. It detects such types by loooking for a
+  // a type is a fancy reference. It detects such types by looking for a
   // nested `wrapped_reference_hint` type.
   struct wrapped_reference_hint
   {};
diff --git a/thrust/thrust/iterator/detail/transform_iterator.inl b/thrust/thrust/iterator/detail/transform_iterator.inl
index 267e878161..a67ccecf75 100644
--- a/thrust/thrust/iterator/detail/transform_iterator.inl
+++ b/thrust/thrust/iterator/detail/transform_iterator.inl
@@ -42,15 +42,14 @@ namespace detail
 template <class UnaryFunc, class Iterator, class Reference, class Value>
 struct make_transform_iterator_base
 {
-private:
-  // FIXME(bgruber): the next line should be correct, but thrust::identity<T> lies and advertises a ::return_type of T,
-  // while its operator() returns const T& (which __invoke_of correctly detects), which causes transform_iterator to
-  // crash during dereferencing.
-  // using wrapped_func_ret_t = ::cuda::std::__invoke_of<UnaryFunc, iterator_value_t<Iterator>>;
-  using wrapped_func_ret_t = result_of_adaptable_function<UnaryFunc(iterator_value_t<Iterator>)>;
+  using func_input_t =
+    ::cuda::std::_If<is_wrapped_reference<::cuda::std::__decay_t<iterator_reference_t<Iterator>>>::value,
+                     const iterator_value_t<Iterator>&, // decay the reference to the value type
+                     iterator_reference_t<Iterator>>;
+  using func_return_t = ::cuda::std::__invoke_of<UnaryFunc, func_input_t>;
 
   // By default, dereferencing the iterator yields the same as the function.
-  using reference  = typename ia_dflt_help<Reference, wrapped_func_ret_t>::type;
+  using reference  = typename ia_dflt_help<Reference, func_return_t>::type;
   using value_type = typename ia_dflt_help<Value, remove_cvref<reference>>::type;
 
 public:
diff --git a/thrust/thrust/iterator/transform_iterator.h b/thrust/thrust/iterator/transform_iterator.h
index 081bf675bb..616106c3d0 100644
--- a/thrust/thrust/iterator/transform_iterator.h
+++ b/thrust/thrust/iterator/transform_iterator.h
@@ -207,9 +207,8 @@ class transform_iterator
   /*! \endcond
    */
 
-public:
-  /*! Null constructor does nothing.
-   */
+  using reference = typename super_t::reference;
+
   transform_iterator() = default;
 
   transform_iterator(transform_iterator const&) = default;
@@ -299,8 +298,24 @@ class transform_iterator
   // See goo.gl/LELTNp
   THRUST_DISABLE_MSVC_WARNING_BEGIN(4172)
 
+  _CCCL_HOST_DEVICE reference dereference() const
+  {
+    // TODO(bgruber): use an if constexpr in C++17
+    return dereference_impl(
+      ::cuda::std::bool_constant<
+        detail::is_wrapped_reference<::cuda::std::__decay_t<iterator_reference_t<Iterator>>>::value>{});
+  }
+
+  _CCCL_EXEC_CHECK_DISABLE
+  _CCCL_HOST_DEVICE
+  reference dereference_impl(::cuda::std::false_type /* iterator does not return a wrapped/proxy reference */) const
+  {
+    return m_f(*this->base());
+  }
+
   _CCCL_EXEC_CHECK_DISABLE
-  _CCCL_HOST_DEVICE typename super_t::reference dereference() const
+  _CCCL_HOST_DEVICE
+  reference dereference_impl(::cuda::std::true_type /* iterator returns a wrapped/proxy reference */) const
   {
     // Create a temporary to allow iterators with wrapped references to
     // convert to their value type before calling m_f. Note that this