diff --git a/include/pybind11/cast.h b/include/pybind11/cast.h
index e8128710e2..bb705ab2d4 100644
--- a/include/pybind11/cast.h
+++ b/include/pybind11/cast.h
@@ -79,6 +79,9 @@ class type_caster<std::reference_wrapper<type>> {
     explicit operator std::reference_wrapper<type>() { return cast_op<type &>(subcaster); }
 };
 
+template <typename type>
+class type_caster<const type> : public type_caster<type> {};
+
 #define PYBIND11_TYPE_CASTER(type, py_name)                                                       \
 protected:                                                                                        \
     type value;                                                                                   \
@@ -907,6 +910,12 @@ struct handle_type_name<kwargs> {
 
 template <typename type>
 struct pyobject_caster {
+    template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>
+    pyobject_caster() : value() {}
+
+    template <typename T = type, enable_if_t<std::is_base_of<object, T>::value, int> = 0>
+    pyobject_caster() : value(reinterpret_steal<type>(handle())) {}
+
     template <typename T = type, enable_if_t<std::is_same<T, handle>::value, int> = 0>
     bool load(handle src, bool /* convert */) {
         value = src;
diff --git a/include/pybind11/pytypes.h b/include/pybind11/pytypes.h
index 324fa932f1..a79b0caadf 100644
--- a/include/pybind11/pytypes.h
+++ b/include/pybind11/pytypes.h
@@ -1784,25 +1784,37 @@ class kwargs : public dict {
     PYBIND11_OBJECT_DEFAULT(kwargs, dict, PyDict_Check)
 };
 
-class set : public object {
+class anyset : public object {
+protected:
+    PYBIND11_OBJECT(anyset, object, PyAnySet_Check)
+
+public:
+    size_t size() const { return static_cast<size_t>(PySet_Size(m_ptr)); }
+    bool empty() const { return size() == 0; }
+    template <typename T>
+    bool contains(T &&val) const {
+        return PySet_Contains(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 1;
+    }
+};
+
+class set : public anyset {
 public:
-    PYBIND11_OBJECT_CVT(set, object, PySet_Check, PySet_New)
-    set() : object(PySet_New(nullptr), stolen_t{}) {
+    PYBIND11_OBJECT_CVT(set, anyset, PySet_Check, PySet_New)
+    set() : anyset(PySet_New(nullptr), stolen_t{}) {
         if (!m_ptr) {
             pybind11_fail("Could not allocate set object!");
         }
     }
-    size_t size() const { return (size_t) PySet_Size(m_ptr); }
-    bool empty() const { return size() == 0; }
     template <typename T>
     bool add(T &&val) /* py-non-const */ {
         return PySet_Add(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 0;
     }
     void clear() /* py-non-const */ { PySet_Clear(m_ptr); }
-    template <typename T>
-    bool contains(T &&val) const {
-        return PySet_Contains(m_ptr, detail::object_or_cast(std::forward<T>(val)).ptr()) == 1;
-    }
+};
+
+class frozenset : public anyset {
+public:
+    PYBIND11_OBJECT_CVT(frozenset, anyset, PyFrozenSet_Check, PyFrozenSet_New)
 };
 
 class function : public object {
diff --git a/include/pybind11/stl.h b/include/pybind11/stl.h
index 51b57a92ba..547e5c0e8f 100644
--- a/include/pybind11/stl.h
+++ b/include/pybind11/stl.h
@@ -49,23 +49,29 @@ forwarded_type<T, U> forward_like(U &&u) {
     return std::forward<detail::forwarded_type<T, U>>(std::forward<U>(u));
 }
 
-template <typename Type, typename Key>
+template <typename Key>
+using make_key_caster = type_caster<conditional_t<std::is_class<intrinsic_t<Key>>::value,
+                                                  const intrinsic_t<Key>,
+                                                  intrinsic_t<Key>>>;
+
+template <typename Type, typename Key, bool Const = false>
 struct set_caster {
     using type = Type;
-    using key_conv = make_caster<Key>;
+    using key_conv = make_key_caster<Key>;
 
     bool load(handle src, bool convert) {
-        if (!isinstance<pybind11::set>(src)) {
+        if (!isinstance<anyset>(src)) {
             return false;
         }
-        auto s = reinterpret_borrow<pybind11::set>(src);
+        auto s = reinterpret_borrow<anyset>(src);
         value.clear();
         for (auto entry : s) {
             key_conv conv;
             if (!conv.load(entry, convert)) {
                 return false;
             }
-            value.insert(cast_op<Key &&>(std::move(conv)));
+            value.insert(
+                std::move(conv).operator typename key_conv::template cast_op_type<Key &&>());
         }
         return true;
     }
@@ -75,23 +81,27 @@ struct set_caster {
         if (!std::is_lvalue_reference<T>::value) {
             policy = return_value_policy_override<Key>::policy(policy);
         }
-        pybind11::set s;
+        typename std::conditional<Const, frozenset, set>::type s;
         for (auto &&value : src) {
             auto value_ = reinterpret_steal<object>(
                 key_conv::cast(forward_like<T>(value), policy, parent));
-            if (!value_ || !s.add(std::move(value_))) {
+            // pybind11::frozenset doesn't have add() for safety, so call PySet_Add directly.
+            if (!value_
+                || PySet_Add(s.ptr(), detail::object_or_cast(std::move(value_)).ptr()) != 0) {
                 return handle();
             }
         }
         return s.release();
     }
 
-    PYBIND11_TYPE_CASTER(type, const_name("Set[") + key_conv::name + const_name("]"));
+    PYBIND11_TYPE_CASTER(type,
+                         const_name<Const>("FrozenSet[", "Set[") + key_conv::name
+                             + const_name("]"));
 };
 
 template <typename Type, typename Key, typename Value>
 struct map_caster {
-    using key_conv = make_caster<Key>;
+    using key_conv = make_key_caster<Key>;
     using value_conv = make_caster<Value>;
 
     bool load(handle src, bool convert) {
@@ -106,7 +116,9 @@ struct map_caster {
             if (!kconv.load(it.first.ptr(), convert) || !vconv.load(it.second.ptr(), convert)) {
                 return false;
             }
-            value.emplace(cast_op<Key &&>(std::move(kconv)), cast_op<Value &&>(std::move(vconv)));
+            value.emplace(
+                std::move(kconv).operator typename key_conv::template cast_op_type<Key &&>(),
+                cast_op<Value &&>(std::move(vconv)));
         }
         return true;
     }
@@ -138,7 +150,7 @@ struct map_caster {
                              + const_name("]"));
 };
 
-template <typename Type, typename Value>
+template <typename Type, typename Value, bool Const = false>
 struct list_caster {
     using value_conv = make_caster<Value>;
 
@@ -174,7 +186,7 @@ struct list_caster {
         if (!std::is_lvalue_reference<T>::value) {
             policy = return_value_policy_override<Value>::policy(policy);
         }
-        list l(src.size());
+        conditional_t<Const, tuple, list> l(src.size());
         ssize_t index = 0;
         for (auto &&value : src) {
             auto value_ = reinterpret_steal<object>(
@@ -182,24 +194,42 @@ struct list_caster {
             if (!value_) {
                 return handle();
             }
-            PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            if (Const) {
+                PyTuple_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            } else {
+                PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            }
         }
         return l.release();
     }
 
-    PYBIND11_TYPE_CASTER(Type, const_name("List[") + value_conv::name + const_name("]"));
+    PYBIND11_TYPE_CASTER(Type,
+                         const_name<Const>("Tuple[", "List[") + value_conv::name
+                             + const_name<Const>(", ...]", "]"));
 };
 
 template <typename Type, typename Alloc>
 struct type_caster<std::vector<Type, Alloc>> : list_caster<std::vector<Type, Alloc>, Type> {};
 
+template <typename Type, typename Alloc>
+struct type_caster<const std::vector<Type, Alloc>>
+    : list_caster<std::vector<Type, Alloc>, Type, true> {};
+
 template <typename Type, typename Alloc>
 struct type_caster<std::deque<Type, Alloc>> : list_caster<std::deque<Type, Alloc>, Type> {};
 
+template <typename Type, typename Alloc>
+struct type_caster<const std::deque<Type, Alloc>>
+    : list_caster<std::deque<Type, Alloc>, Type, true> {};
+
 template <typename Type, typename Alloc>
 struct type_caster<std::list<Type, Alloc>> : list_caster<std::list<Type, Alloc>, Type> {};
 
-template <typename ArrayType, typename Value, bool Resizable, size_t Size = 0>
+template <typename Type, typename Alloc>
+struct type_caster<const std::list<Type, Alloc>>
+    : list_caster<std::list<Type, Alloc>, Type, true> {};
+
+template <typename ArrayType, typename Value, bool Resizable, size_t Size = 0, bool Const = false>
 struct array_caster {
     using value_conv = make_caster<Value>;
 
@@ -238,7 +268,7 @@ struct array_caster {
 
     template <typename T>
     static handle cast(T &&src, return_value_policy policy, handle parent) {
-        list l(src.size());
+        conditional_t<Const, tuple, list> l(src.size());
         ssize_t index = 0;
         for (auto &&value : src) {
             auto value_ = reinterpret_steal<object>(
@@ -246,23 +276,31 @@ struct array_caster {
             if (!value_) {
                 return handle();
             }
-            PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            if (Const) {
+                PyTuple_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            } else {
+                PyList_SET_ITEM(l.ptr(), index++, value_.release().ptr()); // steals a reference
+            }
         }
         return l.release();
     }
 
     PYBIND11_TYPE_CASTER(ArrayType,
-                         const_name("List[") + value_conv::name
+                         const_name<Const>("Tuple[", "List[") + value_conv::name
                              + const_name<Resizable>(const_name(""),
                                                      const_name("[") + const_name<Size>()
                                                          + const_name("]"))
-                             + const_name("]"));
+                             + const_name<Const>(", ...]", "]"));
 };
 
 template <typename Type, size_t Size>
 struct type_caster<std::array<Type, Size>>
     : array_caster<std::array<Type, Size>, Type, false, Size> {};
 
+template <typename Type, size_t Size>
+struct type_caster<const std::array<Type, Size>>
+    : array_caster<std::array<Type, Size>, Type, false, Size, true> {};
+
 template <typename Type>
 struct type_caster<std::valarray<Type>> : array_caster<std::valarray<Type>, Type, true> {};
 
@@ -270,10 +308,18 @@ template <typename Key, typename Compare, typename Alloc>
 struct type_caster<std::set<Key, Compare, Alloc>>
     : set_caster<std::set<Key, Compare, Alloc>, Key> {};
 
+template <typename Key, typename Compare, typename Alloc>
+struct type_caster<const std::set<Key, Compare, Alloc>>
+    : set_caster<std::set<Key, Compare, Alloc>, Key, true> {};
+
 template <typename Key, typename Hash, typename Equal, typename Alloc>
 struct type_caster<std::unordered_set<Key, Hash, Equal, Alloc>>
     : set_caster<std::unordered_set<Key, Hash, Equal, Alloc>, Key> {};
 
+template <typename Key, typename Hash, typename Equal, typename Alloc>
+struct type_caster<const std::unordered_set<Key, Hash, Equal, Alloc>>
+    : set_caster<std::unordered_set<Key, Hash, Equal, Alloc>, Key, true> {};
+
 template <typename Key, typename Value, typename Compare, typename Alloc>
 struct type_caster<std::map<Key, Value, Compare, Alloc>>
     : map_caster<std::map<Key, Value, Compare, Alloc>, Key, Value> {};
diff --git a/tests/test_pytypes.cpp b/tests/test_pytypes.cpp
index d1e9b81a73..8d296f655a 100644
--- a/tests/test_pytypes.cpp
+++ b/tests/test_pytypes.cpp
@@ -75,7 +75,7 @@ TEST_SUBMODULE(pytypes, m) {
     m.def("get_none", [] { return py::none(); });
     m.def("print_none", [](const py::none &none) { py::print("none: {}"_s.format(none)); });
 
-    // test_set
+    // test_set, test_frozenset
     m.def("get_set", []() {
         py::set set;
         set.add(py::str("key1"));
@@ -83,14 +83,26 @@ TEST_SUBMODULE(pytypes, m) {
         set.add(std::string("key3"));
         return set;
     });
-    m.def("print_set", [](const py::set &set) {
+    m.def("get_frozenset", []() {
+        py::set set;
+        set.add(py::str("key1"));
+        set.add("key2");
+        set.add(std::string("key3"));
+        return py::frozenset(set);
+    });
+    m.def("print_anyset", [](const py::anyset &set) {
         for (auto item : set) {
             py::print("key:", item);
         }
     });
-    m.def("set_contains",
-          [](const py::set &set, const py::object &key) { return set.contains(key); });
-    m.def("set_contains", [](const py::set &set, const char *key) { return set.contains(key); });
+    m.def("anyset_size", [](const py::anyset &set) { return set.size(); });
+    m.def("anyset_empty", [](const py::anyset &set) { return set.empty(); });
+    m.def("anyset_contains",
+          [](const py::anyset &set, const py::object &key) { return set.contains(key); });
+    m.def("anyset_contains",
+          [](const py::anyset &set, const char *key) { return set.contains(key); });
+    m.def("set_add", [](py::set &set, const py::object &key) { set.add(key); });
+    m.def("set_clear", [](py::set &set) { set.clear(); });
 
     // test_dict
     m.def("get_dict", []() { return py::dict("key"_a = "value"); });
@@ -310,6 +322,7 @@ TEST_SUBMODULE(pytypes, m) {
                         "list"_a = py::list(d["list"]),
                         "dict"_a = py::dict(d["dict"]),
                         "set"_a = py::set(d["set"]),
+                        "frozenset"_a = py::frozenset(d["frozenset"]),
                         "memoryview"_a = py::memoryview(d["memoryview"]));
     });
 
@@ -325,6 +338,7 @@ TEST_SUBMODULE(pytypes, m) {
                         "list"_a = d["list"].cast<py::list>(),
                         "dict"_a = d["dict"].cast<py::dict>(),
                         "set"_a = d["set"].cast<py::set>(),
+                        "frozenset"_a = d["frozenset"].cast<py::frozenset>(),
                         "memoryview"_a = d["memoryview"].cast<py::memoryview>());
     });
 
diff --git a/tests/test_pytypes.py b/tests/test_pytypes.py
index 5c715ada6b..a6adfdddad 100644
--- a/tests/test_pytypes.py
+++ b/tests/test_pytypes.py
@@ -66,11 +66,12 @@ def test_none(capture, doc):
 
 def test_set(capture, doc):
     s = m.get_set()
+    assert isinstance(s, set)
     assert s == {"key1", "key2", "key3"}
 
+    s.add("key4")
     with capture:
-        s.add("key4")
-        m.print_set(s)
+        m.print_anyset(s)
     assert (
         capture.unordered
         == """
@@ -81,12 +82,43 @@ def test_set(capture, doc):
     """
     )
 
-    assert not m.set_contains(set(), 42)
-    assert m.set_contains({42}, 42)
-    assert m.set_contains({"foo"}, "foo")
+    m.set_add(s, "key5")
+    assert m.anyset_size(s) == 5
 
-    assert doc(m.get_list) == "get_list() -> list"
-    assert doc(m.print_list) == "print_list(arg0: list) -> None"
+    m.set_clear(s)
+    assert m.anyset_empty(s)
+
+    assert not m.anyset_contains(set(), 42)
+    assert m.anyset_contains({42}, 42)
+    assert m.anyset_contains({"foo"}, "foo")
+
+    assert doc(m.get_set) == "get_set() -> set"
+    assert doc(m.print_anyset) == "print_anyset(arg0: anyset) -> None"
+
+
+def test_frozenset(capture, doc):
+    s = m.get_frozenset()
+    assert isinstance(s, frozenset)
+    assert s == frozenset({"key1", "key2", "key3"})
+
+    with capture:
+        m.print_anyset(s)
+    assert (
+        capture.unordered
+        == """
+        key: key1
+        key: key2
+        key: key3
+    """
+    )
+    assert m.anyset_size(s) == 3
+    assert not m.anyset_empty(s)
+
+    assert not m.anyset_contains(frozenset(), 42)
+    assert m.anyset_contains(frozenset({42}), 42)
+    assert m.anyset_contains(frozenset({"foo"}), "foo")
+
+    assert doc(m.get_frozenset) == "get_frozenset() -> frozenset"
 
 
 def test_dict(capture, doc):
@@ -302,6 +334,7 @@ def test_constructors():
         list: range(3),
         dict: [("two", 2), ("one", 1), ("three", 3)],
         set: [4, 4, 5, 6, 6, 6],
+        frozenset: [4, 4, 5, 6, 6, 6],
         memoryview: b"abc",
     }
     inputs = {k.__name__: v for k, v in data.items()}
diff --git a/tests/test_stl.cpp b/tests/test_stl.cpp
index b56a91953b..d818bcc6eb 100644
--- a/tests/test_stl.cpp
+++ b/tests/test_stl.cpp
@@ -248,6 +248,22 @@ TEST_SUBMODULE(stl, m) {
         return v;
     });
 
+    // test_frozen_key
+    m.def("cast_set_map", []() {
+        return std::map<std::set<std::string>, std::string>{{{"key1", "key2"}, "value"}};
+    });
+    m.def("load_set_map", [](const std::map<std::set<std::string>, std::string> &map) {
+        return map.at({"key1", "key2"}) == "value" && map.at({"key3"}) == "value2";
+    });
+    m.def("cast_set_set", []() { return std::set<std::set<std::string>>{{"key1", "key2"}}; });
+    m.def("load_set_set", [](const std::set<std::set<std::string>> &set) {
+        return (set.count({"key1", "key2"}) != 0u) && (set.count({"key3"}) != 0u);
+    });
+    m.def("cast_vector_set", []() { return std::set<std::vector<int>>{{1, 2}}; });
+    m.def("load_vector_set", [](const std::set<std::vector<int>> &set) {
+        return (set.count({1, 2}) != 0u) && (set.count({3}) != 0u);
+    });
+
     pybind11::enum_<EnumType>(m, "EnumType")
         .value("kSet", EnumType::kSet)
         .value("kUnset", EnumType::kUnset);
diff --git a/tests/test_stl.py b/tests/test_stl.py
index 975860b85a..11a445019b 100644
--- a/tests/test_stl.py
+++ b/tests/test_stl.py
@@ -73,6 +73,7 @@ def test_set(doc):
     assert s == {"key1", "key2"}
     s.add("key3")
     assert m.load_set(s)
+    assert m.load_set(frozenset(s))
 
     assert doc(m.cast_set) == "cast_set() -> Set[str]"
     assert doc(m.load_set) == "load_set(arg0: Set[str]) -> bool"
@@ -97,6 +98,38 @@ def test_recursive_casting():
     assert z[0].value == 7 and z[1].value == 42
 
 
+def test_frozen_key(doc):
+    """Test that we special-case C++ key types to Python immutable containers, e.g.:
+    std::map<std::set<K>, V> <-> dict[frozenset[K], V]
+    std::set<std::set<T>> <-> set[frozenset[T]]
+    std::set<std::vector<T>> <-> set[tuple[T, ...]]
+    """
+    s = m.cast_set_map()
+    assert s == {frozenset({"key1", "key2"}): "value"}
+    s[frozenset({"key3"})] = "value2"
+    assert m.load_set_map(s)
+    assert doc(m.cast_set_map) == "cast_set_map() -> Dict[FrozenSet[str], str]"
+    assert (
+        doc(m.load_set_map) == "load_set_map(arg0: Dict[FrozenSet[str], str]) -> bool"
+    )
+
+    s = m.cast_set_set()
+    assert s == {frozenset({"key1", "key2"})}
+    s.add(frozenset({"key3"}))
+    assert m.load_set_set(s)
+    assert doc(m.cast_set_set) == "cast_set_set() -> Set[FrozenSet[str]]"
+    assert doc(m.load_set_set) == "load_set_set(arg0: Set[FrozenSet[str]]) -> bool"
+
+    s = m.cast_vector_set()
+    assert s == {(1, 2)}
+    s.add((3,))
+    assert m.load_vector_set(s)
+    assert doc(m.cast_vector_set) == "cast_vector_set() -> Set[Tuple[int, ...]]"
+    assert (
+        doc(m.load_vector_set) == "load_vector_set(arg0: Set[Tuple[int, ...]]) -> bool"
+    )
+
+
 def test_move_out_container():
     """Properties use the `reference_internal` policy by default. If the underlying function
     returns an rvalue, the policy is automatically changed to `move` to avoid referencing