What's the difference between these two functions? I've seen people put quotes around type annotations and other times leave them out but I couldn't find why people choose to use one or the other.

def do_something(entity: Entity):pass
def do_something(entity: 'Entity'):pass

Are there advantages or disadvantages to any of these?

Putting quotes around type hints is something that makes sense when making a Forward Reference according to PEP 484. In this case putting quotes around a name is used to subdue a NameError that would occur.

In other cases, don't use quotes, it doesn't result in the hint you want:

>>> def bad_foo(a: 'int'):
...     pass
>>> def good_foo(a: int):
...     pass
>>> bad_foo.__annotations__['a'] == good_foo.__annotations__['a']
False

though for now type checkers (mypy, atleast) don't seem to treat these differently, I wouldn't be sure if that would be the case in the future. Best to be clear and not use quotes when you actually don't need them.