Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
The classical and quantum theories of synchrotron radiation (SR) are reviewed. A concise history of the development and discovery of SR, and its fundamental properties, are given. The emphasis is placed on the quantum effects: quantum fluctuations of trajectories of electrons, and radiative polarization of electrons and positrons in storage rings. The theories of undulator radiation and radiation in a short magnet are discussed in brief. Experimental investigations of synchrotron radiation and its applications in physical experiments are reviewed.