The authors discuss the technological problems associated with the use of fast neutrons in radiotherapy of cancer patients and outline the approaches to the solution of these problems. The state of the art is assessed. Physical and radiobiological prerequisites for the use of fast reactors for radiotherapy of patients with malignant tumors are analyzed. Results of clinical use of BR-10 reactor at the Medical Radiology Research Center, Russian Academy of Medical Sciences, are presented. Experimental and clinical findings indicate that the results of radiotherapy may be appreciably improved if a novel perspective source of fast neutrons, a nuclear reactor, is used.