Squirrels live on acorns, hickory nuts, walnuts, beechnuts and other nuts. Squirrels are very savvy with their nuts. "The Seattle Times" says they can tell which nuts are the most perishable and eat those first. They have a very good sense of smell, which allows them to smell nuts buried in the ground. Before burying a nut, the squirrel rubs it with its face to mark it with a scent that the squirrel can later identify.