The article sets forth the theory of the influence of multiple scattering on the radiation of ultrarelativistic particles in matter. The classical theory of the Landau-Pomeranchuk effect of suppression of the radiation of relativistic particles in an amorphous medium is presented both in the simple form given by the authors and in a refined form due to Migdal. It is shown that in investigation of the influence of multiple scattering on the radiation of fast particles in matter it is possible to use a functional integration method which permits construction of a quantitative theory of the effect in both amorphous and crystalline media. The question of the possibility of stochastic motion of fast charged particles in a crystal is discussed. The general regularities and distinctive features in processes of radiation of relativistic particles in amorphous and crystalline media and also in intense external electromagnetic fields are discussed.