Do Cats Hunt Squirrels?

So, I'm wondering if anyone has any experience with their
cats hunting squirrels?

The squirrels love to sit on the back fence and taunt the cats and make
them chase them. The squirrels have much better footing on the top of
the fence and sometiimes the cats fall off into the blackberry bushes.
Even though the cats never win, both they and the squirrels seem to
enjoy the game. When the cats get too close the squirrels jump off onto
a tree and yell at the cats from there.

However, in the front yard, where there is an oak tree, the squirells
have free reign to the yard to gather and bury the acorns and the cats
just watch them and never chase them.