There are three variants of `TypeVar`s:

(1) TypeVars that are neither constrained nor bound: `T = TypeVar("T")`
(2) TypeVars that are bound: `U = TypeVar("U", bound=str)`
(3) TypeVars that are constrained: `V = TypeVar("V", str, bytes)`

The third variant is important for annotating certain functions, such as those in the `re` module. However, it has a number of issues (see https://github.com/python/typing/discussions/1080 for further discussion):

(1) It has somewhat surprising semantics in many situations.
(2) It is difficult for type checkers to deal with, leading to a number of bugs in mypy, for example.
(3) Many users (especially people relatively inexperienced with Python typing) reach for constrained TypeVars in situations where using bound TypeVars or the @overload decorator would be more appropriate.

Both PEP 484 and the documentation for the typing module, however:

(1) Give examples for variants (1) and (3), but not for variant (2), which is treated as something of an afterthought.
(2) Do not mention that TypeVars can be bound to a union of types, which is an important point: `T = TypeVar("T", str, bytes)` has different semantics to `T = TypeVar("T", bound=str|bytes)`, and often the latter is more appropriate.

Maybe historically constrained type vars predated bound type vars. This could have influenced the way PEP 484 was written and then the docs were derived from the PEP.

But yes, this should be fixed in as many places as possible (including the mypy docs, probably).

I would even support a minor update to PEP 484 to help people find the right way (the PEP is still widely cited). It would have to be just be a textual change, not a spec change.

New changeset 81b425d4dc43b60dd11a3e9abc5c84a4b8b384db by Alex Waygood in branch 'main':
bpo-46769: Improve documentation for `typing.TypeVar` (GH-31712)
https://github.com/python/cpython/commit/81b425d4dc43b60dd11a3e9abc5c84a4b8b384db

New changeset d5ed8a8258eaf7a241978b1b0aeb971108d0f7e0 by Alex Waygood in branch '3.10':
[3.10] bpo-46769: Improve documentation for `typing.TypeVar` (GH-31712) (GH-31941)
https://github.com/python/cpython/commit/d5ed8a8258eaf7a241978b1b0aeb971108d0f7e0

New changeset 0bbb6956f83ef457872b8f04242bb02b6898350d by Jelle Zijlstra in branch '3.9':
[3.9] bpo-46769: Improve documentation for `typing.TypeVar` (GH-31712) (GH-31941) (GH-32067)
https://github.com/python/cpython/commit/0bbb6956f83ef457872b8f04242bb02b6898350d

Thanks Alex for the PR and Łukasz for merging the last backport!

Thanks Guido for your insight, and Jelle/Łukasz for the reviews and backports!

I'm on holiday right now, but when I'm back, I'll take a look at maybe proposing some minor revisions to PEP 484 as well, as Guido suggests.

New changeset 80af26d25af5568229d31ecb2a8f1bf9702b7791 by Ken Jin in branch '3.10':
[3.10] bpo-46769: Fix backticks in typing.rst to appease rstlint (GH-32374)
https://github.com/python/cpython/commit/80af26d25af5568229d31ecb2a8f1bf9702b7791

New changeset d6a7ee69fb3263450ba47bed9104f4a68a08a9bd by Ken Jin in branch '3.9':
[3.9] bpo-46769: Fix backticks in typing.rst to appease rstlint (GH-32375)
https://github.com/python/cpython/commit/d6a7ee69fb3263450ba47bed9104f4a68a08a9bd