We have a major problem with them up North....

We live on an island, and since the wolves left there is nothing eating
the red squirrels. They have learned to use our cat door, and they come in the house all the time, run around, break things. One even jumped on the screened window near my head when I was napping, and scared the beejeebers out of me.

We have used a Havahart trap twice....last year we took 11 off and dumped them on another island. 2 years before that we did 17 !

Some of our cousins SHOOT them, and the locals SHOOT them because they chew the electrical and telephone wires in the winter.

We raised a baby orphan squirrel once when my son was little. We took him to show and tell etc. But boy did he STINK! The smell was AWFUL....
I couldn't deal with him for long, so I took him to the Human Society.
When you see those cute videos....you do not get a sense of the SMELL! WHEW.

We have some tame gray squirrels...they are not so damaging. So I don't mind them. We even feed those.