Since 1971 with the invention of the CT scanner, mathematics has played a large role in medicine. After a brief review of the mathematical ideas involved in CT, I will review emission tomography and magnetic resonance imaging (MRI) and then discuss a project in functional MRI ("functional'' is not in the sense of Banach but in the sense of trying to learn where in the brain higher cognition takes place). Finally, I will present some present approaches to the currently hot problem of making a closed loop control system for diabetics: an algorithm for driving an insulin pump using blood glucose measurements.