Most people do not realize that many substances they use in the kitchen and the bathroom are not simple liquids or solids. Everyone is familiar with three states of matter: solids, liquids, and gases. However, creams, shampoo, toothpaste, and ketchup all have properties of both liquids and solids. This paper describes demonstrations and laboratory exercises that show intriguing properties of squishy substances, defined as materials that are not unambiguously solid, liquid, or gas. Unlike some areas of physics, the concepts behind squishy materials are understandable even by beginning students. Squishy physics can be used to show physics questions arising from everyday life and to convey the excitement of current research.