This study presents an interpretation of classical and quantum theories of fast charged particle radiation in an external field. Various methods describing the process of particle interaction with substance and external fields are analyzed, such as Born approximation, the Schwinger operator method and different versions of the quasi-classical approximation. Such problems as time evolution of an electromagnetic field applied to and emitting electrons, coherence length, radiation in the simplest external fields, Vavilov-Cherenkov radiation and the correspondence of different methods describing the interaction between fast particles and matter are also considered.