In recent decades there have been many advances in methods for the prevention, diagnosis, and treatment of diseases. These advances have resulted in improved health care for many patients, including longer lifespan and a better quality of life. They have also increased the complexity of medical decisions and created an opportunity for industrial and systems engineering (ISE) and operations research (OR) methods to assist medical decision making. This article summarizes some of the active areas of research and describes several examples of open problems.