We describe several radiation processes in media excited by volume and surface acoustic waves. They include the Cherenkov and transition radiations on acoustic superlattices, transition radiation on an interface with a dynamical periodic structure, the Smith-Purcell radiation on surface waves, bremsstrahlung of high-energy electrons and the creation of electron-positron pairs by high energy photons in crystals in the presence of hypersonic waves. The conditions on the parameters of acoustic fields are specified under which their influence is essential. All these considerations show that the acoustic waves can serve as an efficient mechanism to control the parameters of various kinds of radiation processes.