Analysis of the physical properties of surfaces should be based on the maximum possible amount of information deduced from studies of the propagation of surface rather than volume electromagnetic waves, in which the energy is transported only along surfaces or separation boundaries between media. The present review, therefore, discusses a broad range of problems in the crystal optics of surface electromagnetic waves (surface polaritons), a subject developed in the course of the last few years. Various theoretical and experimental methods of investigating surface waves in crystals are discussed and compared, including a detailed review of Raman scattering of light. Other topics discussed include different effects in the spectra of surface waves due to the transition layer, the role of damping and spatial dispersion, the transformation of surface into volume waves, and so on. Possible fields of future research are suggested.