diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 3579da155..f09b5febb 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -602,6 +602,12 @@ NAMESPACE_END(detail)
 \endrst */
 class iterator : public object {
 public:
+    using iterator_category = std::input_iterator_tag;
+    using difference_type = ssize_t;
+    using value_type = handle;
+    using reference = const handle;
+    using pointer = const handle *;
+
     PYBIND11_OBJECT_DEFAULT(iterator, object, PyIter_Check)
 
     iterator& operator++() {
@@ -615,7 +621,7 @@ public:
         return rv;
     }
 
-    handle operator*() const {
+    reference operator*() const {
         if (m_ptr && !value.ptr()) {
             auto& self = const_cast<iterator &>(*this);
             self.advance();
@@ -623,7 +629,7 @@ public:
         return value;
     }
 
-    const handle *operator->() const { operator*(); return &value; }
+    pointer operator->() const { operator*(); return &value; }
 
     /** \rst
          The value which marks the end of the iteration. ``it == iterator::sentinel()``
diff --git a/tests/test_sequences_and_iterators.cpp b/tests/test_sequences_and_iterators.cpp
index 640188240..cda0af479 100644
--- a/tests/test_sequences_and_iterators.cpp
+++ b/tests/test_sequences_and_iterators.cpp
@@ -290,4 +290,14 @@ test_initializer sequences_and_iterators([](py::module &pm) {
         }
         return l;
     });
+
+    // Make sure that py::iterator works with std algorithms
+    m.def("count_none", [](py::object o) {
+        return std::count_if(o.begin(), o.end(), [](py::handle h) { return h.is_none(); });
+    });
+
+    m.def("find_none", [](py::object o) {
+        auto it = std::find_if(o.begin(), o.end(), [](py::handle h) { return h.is_none(); });
+        return it->is_none();
+    });
 });
diff --git a/tests/test_sequences_and_iterators.py b/tests/test_sequences_and_iterators.py
index b340451d7..306664751 100644
--- a/tests/test_sequences_and_iterators.py
+++ b/tests/test_sequences_and_iterators.py
@@ -113,3 +113,7 @@ def test_python_iterator_in_cpp():
     with pytest.raises(RuntimeError) as excinfo:
         m.iterator_to_list(iter(bad_next_call, None))
     assert str(excinfo.value) == "py::iterator::advance() should propagate errors"
+
+    l = [1, None, 0, None]
+    assert m.count_none(l) == 2
+    assert m.find_none(l) is True