diff --git a/src/inspect/types.rs b/src/inspect/types.rs
index 6dfe88477f8..eb7bdd40cb6 100644
--- a/src/inspect/types.rs
+++ b/src/inspect/types.rs
@@ -399,6 +399,7 @@ mod test {
 mod conversion {
     use crate::inspect::types::test::assert_display;
     use crate::{FromPyObject, IntoPy};
+    use std::collections::{HashMap, HashSet};
 
     #[test]
     fn unsigned_int() {
@@ -459,4 +460,18 @@ mod conversion {
         assert_display(&<&[u8]>::type_output(), "bytes");
         assert_display(&<&[u8]>::type_input(), "bytes");
     }
+
+    #[test]
+    fn collections() {
+        assert_display(&<Vec<usize>>::type_output(), "List[int]");
+        assert_display(&<Vec<usize>>::type_input(), "Sequence[int]");
+
+        assert_display(&<HashSet<usize>>::type_output(), "Set[int]");
+        assert_display(&<HashSet<usize>>::type_input(), "Set[int]");
+
+        assert_display(&<HashMap<usize, f32>>::type_output(), "Dict[int, float]");
+        assert_display(&<HashMap<usize, f32>>::type_input(), "Mapping[int, float]");
+
+        assert_display(&<(usize, f32)>::type_input(), "Tuple[int, float]");
+    }
 }
diff --git a/src/types/dict.rs b/src/types/dict.rs
index bd75d89722b..3bfd3b84813 100644
--- a/src/types/dict.rs
+++ b/src/types/dict.rs
@@ -3,6 +3,7 @@
 use super::PyMapping;
 use crate::err::{self, PyErr, PyResult};
 use crate::ffi::Py_ssize_t;
+use crate::inspect::types::TypeInfo;
 use crate::types::{PyAny, PyList};
 #[cfg(not(PyPy))]
 use crate::IntoPyPointer;
@@ -361,6 +362,10 @@ where
             .map(|(k, v)| (k.into_py(py), v.into_py(py)));
         IntoPyDict::into_py_dict(iter, py).into()
     }
+
+    fn type_output() -> TypeInfo {
+        TypeInfo::dict_of(K::type_output(), V::type_output())
+    }
 }
 
 impl<K, V> IntoPy<PyObject> for collections::BTreeMap<K, V>
@@ -374,6 +379,10 @@ where
             .map(|(k, v)| (k.into_py(py), v.into_py(py)));
         IntoPyDict::into_py_dict(iter, py).into()
     }
+
+    fn type_output() -> TypeInfo {
+        TypeInfo::dict_of(K::type_output(), V::type_output())
+    }
 }
 
 /// Conversion trait that allows a sequence of tuples to be converted into `PyDict`
@@ -451,6 +460,10 @@ where
         }
         Ok(ret)
     }
+
+    fn type_input() -> TypeInfo {
+        TypeInfo::mapping_of(K::type_input(), V::type_input())
+    }
 }
 
 impl<'source, K, V> FromPyObject<'source> for BTreeMap<K, V>
@@ -466,6 +479,10 @@ where
         }
         Ok(ret)
     }
+
+    fn type_input() -> TypeInfo {
+        TypeInfo::mapping_of(K::type_input(), V::type_input())
+    }
 }
 
 #[cfg(test)]
diff --git a/src/types/list.rs b/src/types/list.rs
index 2538833dec7..40e717ef9a7 100644
--- a/src/types/list.rs
+++ b/src/types/list.rs
@@ -6,6 +6,7 @@ use std::convert::TryInto;
 
 use crate::err::{self, PyResult};
 use crate::ffi::{self, Py_ssize_t};
+use crate::inspect::types::TypeInfo;
 use crate::internal_tricks::get_ssize_index;
 use crate::types::PySequence;
 use crate::{
@@ -368,6 +369,10 @@ where
         let list = new_from_iter(py, &mut iter);
         list.into()
     }
+
+    fn type_output() -> TypeInfo {
+        TypeInfo::list_of(T::type_output())
+    }
 }
 
 #[cfg(test)]
diff --git a/src/types/sequence.rs b/src/types/sequence.rs
index dcc4a2e729c..b6b9e4429e8 100644
--- a/src/types/sequence.rs
+++ b/src/types/sequence.rs
@@ -1,6 +1,7 @@
 // Copyright (c) 2017-present PyO3 Project and Contributors
 use crate::err::{self, PyDowncastError, PyErr, PyResult};
 use crate::exceptions::PyValueError;
+use crate::inspect::types::TypeInfo;
 use crate::internal_tricks::get_ssize_index;
 use crate::types::{PyAny, PyList, PyString, PyTuple};
 use crate::{ffi, PyNativeType, ToPyObject};
@@ -275,6 +276,10 @@ where
         }
         extract_sequence(obj)
     }
+
+    fn type_input() -> TypeInfo {
+        TypeInfo::sequence_of(T::type_input())
+    }
 }
 
 fn extract_sequence<'s, T>(obj: &'s PyAny) -> PyResult<Vec<T>>
diff --git a/src/types/set.rs b/src/types/set.rs
index cf97eb484f0..6f425559578 100644
--- a/src/types/set.rs
+++ b/src/types/set.rs
@@ -2,6 +2,7 @@
 //
 
 use crate::err::{self, PyErr, PyResult};
+use crate::inspect::types::TypeInfo;
 #[cfg(Py_LIMITED_API)]
 use crate::types::PyIterator;
 use crate::{ffi, AsPyPointer, FromPyObject, IntoPy, PyAny, PyObject, Python, ToPyObject};
@@ -271,6 +272,10 @@ where
         }
         set.into()
     }
+
+    fn type_output() -> TypeInfo {
+        TypeInfo::set_of(K::type_output())
+    }
 }
 
 impl<'source, K, S> FromPyObject<'source> for HashSet<K, S>
@@ -282,6 +287,10 @@ where
         let set: &PySet = ob.downcast()?;
         set.iter().map(K::extract).collect()
     }
+
+    fn type_input() -> TypeInfo {
+        TypeInfo::set_of(K::type_input())
+    }
 }
 
 impl<K> IntoPy<PyObject> for BTreeSet<K>
@@ -297,6 +306,10 @@ where
         }
         set.into()
     }
+
+    fn type_output() -> TypeInfo {
+        TypeInfo::set_of(K::type_output())
+    }
 }
 
 impl<'source, K> FromPyObject<'source> for BTreeSet<K>
@@ -307,6 +320,10 @@ where
         let set: &PySet = ob.downcast()?;
         set.iter().map(K::extract).collect()
     }
+
+    fn type_input() -> TypeInfo {
+        TypeInfo::set_of(K::type_input())
+    }
 }
 
 #[cfg(test)]
diff --git a/src/types/tuple.rs b/src/types/tuple.rs
index b198da72bdd..84165e1fce3 100644
--- a/src/types/tuple.rs
+++ b/src/types/tuple.rs
@@ -3,6 +3,7 @@
 use std::convert::TryInto;
 
 use crate::ffi::{self, Py_ssize_t};
+use crate::inspect::types::TypeInfo;
 use crate::internal_tricks::get_ssize_index;
 use crate::types::PySequence;
 use crate::{
@@ -293,6 +294,10 @@ macro_rules! tuple_conversion ({$length:expr,$(($refN:ident, $n:tt, $T:ident)),+
                ret
             }
         }
+
+        fn type_output() -> TypeInfo {
+            TypeInfo::Tuple(Some(vec![$( $T::type_output() ),+]))
+        }
     }
 
     impl <$($T: IntoPy<PyObject>),+> IntoPy<Py<PyTuple>> for ($($T,)+) {
@@ -304,6 +309,10 @@ macro_rules! tuple_conversion ({$length:expr,$(($refN:ident, $n:tt, $T:ident)),+
                 ret
             }
         }
+
+        fn type_output() -> TypeInfo {
+            TypeInfo::Tuple(Some(vec![$( $T::type_output() ),+]))
+        }
     }
 
     impl<'s, $($T: FromPyObject<'s>),+> FromPyObject<'s> for ($($T,)+) {
@@ -320,6 +329,10 @@ macro_rules! tuple_conversion ({$length:expr,$(($refN:ident, $n:tt, $T:ident)),+
                 Err(wrong_tuple_length(t, $length))
             }
         }
+
+        fn type_input() -> TypeInfo {
+            TypeInfo::Tuple(Some(vec![$( $T::type_input() ),+]))
+        }
     }
 });