Purely nuclear diffraction of synchrotron radiation enables the glow of excited atomic nuclei to be observed in the absence of background nonresonant electron scattering. Nuclei excited in an iron borate crystal can generate in the crystal directed gamma radiation with a narrow spectral band. Based on the remarkable properties of iron borate, the first source of synchrotron Mössbauer (SM) radiation was created a quarter of a century ago. The history of the emergence and development of a new branch of optics — quantum optics of resonant gamma radiation — is briefly reviewed, the physical concepts underlying operation of the SM radiation source are presented, and the design of such a source deployed in the optical line of the European Synchrotron Center (ESRF) is described. Options for using SM radiation in the physics of the condensed state of matter, quantum optics, geophysics, planetology, and other areas of research are presented.