The use of cyclotrons and synchrotrons to accelerate charged particles in hospital settings for the purpose of cancer therapy is increasing. Consequently, there is a growing demand from medical physicists, radiographers, physicians and oncologists for articles that explain the basic physical concepts of these technologies. There are unique advantages and disadvantages to all methods of acceleration. Several promising alternative methods of accelerating particles also have to be considered since they will become increasingly available with time; however, there are still many technical problems with these that require solving. This article serves as an introduction to this complex area of physics, and will be of benefit to those engaged in cancer therapy, or who intend to acquire such technologies in the future.