They are a problem in my yard just about every year. Except for the year we had a pair of hawks nesting nearby. That was awesome. The starlings thinned out considerably that summer as well. I was really hoping the hawks would set up long term residence, but no luck.
They feast on our apple trees, and get the idea that they own the territory. They chewed my hammock to ribbons last summer, and a day later chewed a hole through the kitchen screen window to get to the fresh bread on my counter. And it got to the point that my kids wouldn't go outside and play because the danged squirrels were being so aggressive. We live in the city limits, but discovered that if you shoot squirrels with a .22 on the 4th of July, the neighbors just assume it's noise from fireworks.