When squirrels invade your house or other buildings they can do extensive damage. They can get into many homes, and once there are difficult to eliminate and deter. If squirrels discover a partial entrance such as a broken window, a construction gap, a roof vent, a damaged piece of trim, or loose roofing, they'll finish the job and enlarge the entrance into your home. They can get into anything they can fit their head through. The space between the facia board and the roof is the most vulnerable to them. Once in a while they will cause damage to insulation, rafters and electric wires.
If you get squirrels in your house you've got to get them out. Squirrels are diurnal and are outside most of the day. You may be able to close off their entrance when they are out or you may install a one-way exit over the entrance. Often the only practical way is to remove the squirrels, dead or alive, through trapping. Then you must make immediate repairs to close the entrance hole(s). Large rat traps, Conibear 55 or 110 traps, or No. 0 or No. 1 leg hold traps will provide a lethal solution. Havahart type live traps may also be used, but then what do you do with the squirrel? You can kill it or relocate it. Technically re-location is illegal, not advisable biologically, and who wants to inherit your problem? Best trap baits are sunflower seeds, peanut butter, nuts, anise oil, shelled corn, or slices of apple.
If a squirrel falls down a chimney or stove pipe and can't get out, lower a braided rope down to the bottom and leave it. They'll usually climb up the rope and out within a few hours.