Papers on acousto-optical phenomena in solids and their most important applications to research in solid state physics and to modern technology are surveyed. The theory of the diffraction of electromagnetic waves by sound in isotropic and anisotropic solids is discussed. In addition to such ``classical'' special cases of diffraction as Bragg and Raman--Nath diffraction, we also consider some cases of the diffraction of light by sound in which the reflection of light at the faces of the crystal and modulation of the light by the sound wave have an important effect on the nature of the acousto-optical interaction. The contribution of the electron density wave accompanying a sound wave in piezoactive semiconductors is considered and features of this acousto-optical interaction mechanism are discussed. The quantum theory of the diffraction of light by sound is examined. Microscopic expressions for the photoelasticity constants are obtained and the resonance characteristics of these constants at photon energies close to the width of the forbidden gap in the crystal are investigated. In the experimental part of the paper we review various methods of investigating the diffraction of light by sound in solids and present the basic results in this field together with examples of the use of acousto-optical methods in various areas of solid state physics. In the concluding section we examine some important applications of the diffraction of light by sound to modern optical and electronic systems.