Part I of this review monograph deals with the Vavilov-Cherenkov effect theory. The monograph details the classical Tamm-Frank theory of Vavilov-Cherenkov radiation in an isotropic medium, as well as the quantum theory of Vavilov-Cherenkov radiation, first developed by V. L. Ginzburg, and the reverse Vavilov-Cherenkov effect, considered by I. E. Tamm. In addition, questions of theory in an anisotropic medium are raised. The main properties of radiation in isotropic and anisotropic media and their experimental verification are considered in detail. The monograph is intended for experimental physicists working with high-energy particles, but may be useful for a wider range of physicists interested in the Vavilov-Cherenkov effect.