The article is the first review in the world's literature of research on diffraction of M\"ossbauer $\gamma$ rays in crystals. This field of research has developed recently and independently, and has involved both experimental and theoretical studies. Its development is due, on the one hand, to the unique possibilities provided by M\"ossbauer radiation for investigation of the nature of a number of phenomena of solid-state physics and nuclear physics and, on the other hand, to the alluring promise of use of M\"ossbauer radiation diffraction in applications. The review discusses the current state of research and the most important directions of the studies. These include studies, important in investigation of crystal structure, on determination of the phase of the x-ray structure factor, on the structure of magnetic and electric fields in crystals, on separation of coherent elastic and inelastic scattering of $\gamma$ rays in crystals, and on coherent Coulomb excitation of low-lying nuclear levels. The research described is promising in applications and shows that a new diffraction method is in the process of being established--M\"ossbauerography, which has a number of interesting possibilities and is a useful addition to traditional diffraction methods of research such as x-ray and neutron diffraction. The phenomenon of suppression of the inelastic channels of nuclear reactions in Mössbauer diffraction is discussed in detail. Most of the article is devoted to exposition of the theory of the phenomena mentioned and to the specific properties of M\"ossbauer coherent scattering which distinguish it from diffraction of other types of radiation in crystals.