The article presents the history of creation, formation and development of the State Scientific Center of the Russian Federation — Federal Medical Biophysical Center named after A.I. Burnazyan of the Federal Medical and Biological Agency of Russia (A.I. Burnazyan Federal Biophysical Center, the Center). The Institute of Biophysics of USSR Ministry of Health and Clinical Hospital № 6, predecessors of the Center, were engaged in the elimination of medical and sanitary consequences of Chernobyl Radiation Accident (1986). The main directions of activities of the A.I. Burnazian Federal Medical Biophysical Center — the flagship institution of Russian health care in the field of biophysics, radiation and nuclear medicine are considered. The perspectives of scientific activity of the Center related to solving actual problems of modern radiobiology, radiation safety and biomedical technologies are outlined. It is concluded that it is expedient to create the Disaster Medicine Service of the Federal Medical and Biomedical Agency of Russia.