After a short historical note on the origins of radiotherapy, this paper reviews the main specifications of radiations used for therapy. One main characteristic is the dose distribution in the patient's body, the other is the so-called "oxygen enhancement ratio" (O.E.R.) which is related to the linear energy transfer (L.E.T.). High energy heavy ions beams seem to present an ideal combination of those parameters. However the relatively short range of heavy ions requires the use of high energies and, therefore, of large and costly accelerators. After examining the basic requirements of heavy ion therapy accelerators, the main existing projects for such accelerators are briefly reviewed.