The application of genetic and evolutionary computation to problems in medicine has increased rapidly over the past five years, but there are specific issues and challenges that distinguish it from other real-world applications. Obtaining reliable and coherent patient data, establishing the clinical need and demonstrating value in the results obtained are all aspects that require careful and detailed consideration. This tutorial is based on research which uses genetic programming (a representation of Cartesian Genetic Programming) in the diagnosis and monitoring of Parkinson's disease, Alzheimer's disease and other neurodegenerative conditions, as well as in the early detection of breast cancer through automated assessment of mammograms. The work is supported by multiple clinical studies in progress in the UK (Leeds General Infirmary), USA (UCSF), UAE (Dubai Rashid Hospital), Australia (Monash Medical Center) and Singapore (National Neuroscience Institute). The technology is protected through three patent applications and a University spin-out company marketing four medical devices. The tutorial considers the following topics: Introduction to medical applications of genetic and evolutionary computation and how these differ from other real-world applications Overview of past work in the from a medical and evolutionary computation point of view Three case examples of medical applications: i. diagnosis and monitoring of Parkinson's disease ii. detection of beast cancer from mammograms iii. cancer screening using Raman spectroscopy Practical advice on how to get started working on medical applications, including existing medical databases and conducting new medical studies, commercialization and protecting intellectual property. Summary, further reading and links