The Mössbauer effect, the recoilless absorption and emission of gamma rays by nuclei embedded in solids, has its origin in the properties of the solid state. The nature of this connection is dealt with in some detail and the various effects of the crystalline environment on the nuclear energy levels is described. The importance of these effects as contributions to the study of the physical and chemical properties of crystals is discussed, and applications which depend on the intrinsic energy resolution of the effect are described. The recoilless nuclear resonant scattering and diffraction of gamma rays is also dealt with in some detail.