The theory of the Vavilov-Cherenkov radiation observed by Cherenkov in 1934 was created by Tamm, Frank and Ginsburg who associated the observed blue light with the uniform charge motion of a charge at a velocity greater than the velocity of light in the medium. On the other hand, Vavilov, Cherenkov's teacher, attributed the observed blue light to the deceleration of electrons. This has given rise to the appearance of papers in which the radiation of a charge uniformly moving in a finite space interval was related to the Bremsstrahlung arising at the end points of the motion interval. This monograph is intended for students of the third year and higher, for postgraduates, for professional scientists (both experimentalists and theoreticians) dealing with Vavilov-Cherenkov and synchrotron radiation. An acquaintance with the three volumes of the Landau and Lifshitz course (Quantum Mechanics, Classical Field Theory and Macroscopic Electrodynamics) is sufficient for understanding the text.