Experimental and theoretical work on the scattering of Mossbauer y radiation by condensed matter is reviewed, covering the period from 1958, and the subject is presented as having features akin to those of x-ray diffraction, inelastic neutron scattering and Mossbauer absorption spectroscopy. An outline of theoretical work on coherence and recoil effects for both electronic and nuclear resonant scattering is given. This is followed by a review of experiments on electronic (Rayleigh) scattering covering thermal diffuse scattering in crystals, Debye-Waller factors, soft modes and critical scattering, diffusion phenomena and amorphous materials, and plastic and liquid crystals, and a review of experiments on nuclear resonant scattering covering coherence interference and diffraction, the crystallographic phase problem, magnetic and quadrupole Mossbauer diffraction, dynamic theory and multiple scattering, cooperative excitation, refractive index, time domain experiments, and experiments based on detection of the conversion electrons.