We all sleep: but what is it? How much do you need? Are you a 'lark' or an 'owl'? What is 'social jetlag' and do you suffer from it? In this talk I will review some of the existing mathematical models of the sleep/wake cycle and the body clock. I will show how they are intriguing examples of nonsmooth dynamical systems and discuss how mathematical models can help us understand the biological mechanisms that underlie sleep timing and duration and address policy questions such as whether we should move school start times for adolescents.