We review the results of studies of spontaneous and stimulated emission of relativistic particles in natural and photonic crystals.We consider the diffraction of electromagnetic waves in a crystal, and the resonance and parametric (quasi-Cherenkov) X-ray radiation, the radiation in the channeling of relativistic particles in crystals, diffraction radiation in conditions of channeling, diffraction radiation of a relativistic oscillator, induced radiation in multidimensional space-periodic resonators (natural or artificial (electromagnetic, photonic) crystals).
