Optimal mass transport methods have recently become very important for various problems in medical imaging analysis including registration and anatomical shape. They have been included in software packages, e.g., the 3D Slicer of the Harvard Medical School. We will describe some of the key issues in medical imaging, and how optimal mass transport can be used to shed some light on the solution of these problems. Applications include left atrial fibrillation, traumatic brain injury, and tumor growth models. Very fast implementations using GPUs, even make these methods suitable in an intraoperative setting.