This is an expanded text of papers presented in Berlin on March 2, 1979 at a session of the Academy of Sciences and Physical Society of the DDR celebrating the 100th anniversary of Einstein's birth, and also on March 28, 1979 in Moscow at a scientific session of the Division of General Physics and Astronomy and the Division of Nuclear Physics of the Academy of Sciences of the USSR. Some points of the special theory of relativity and the quantum theory of radiation are treated. Primarily two problems are treated: the problem of a velocity exceeding the velocity of light in a vacuum, and the Doppler effect in a medium in its classical and quantum interpretations.