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A review of the results studies on luminescence of mainly natural diamonds under X-ray excitation is presented. Such luminescence of diamond crystals is widely used in separation of diamond-bearing ores in diamond mining industry. Diamonds contain numerous luminescence centers that can be excited by optical radiation. Photoluminescence (PL) is characterized by wide variety of properties. It is difficult to discern PL of diamonds from PL of accompanying minerals and provide sufficient extraction selectivity. The first comparative studies of the properties of X-ray excited luminescence (XL) and photoluminescence, carried out in the last century, showed the properties of XL are much less diverse. X-ray luminescence spectra of most natural diamonds contain mainly one band, so-called A-band, visually perceived as blue emission. Spectral bands and lines observed in photoluminescence appear additionally in XL spectra of some samples. Some samples do not exhibit A-band in XL. The specific properties of XL of diamonds determined the capability of usage of XL in separation of diamond-bearing ores. In the mid-sixties, an idea stating the donor-acceptor process of emission of the A-band under X-ray excitation had appeared. This idea has been disputed on the basis of detailed study of kinetics and other properties of XL, but the concept of the donor-acceptor process has been circulating in various publications for several decades. The review presents the temperature dependences of the decay time constants of individual components of X-ray excited luminescence, which as a whole should be considered as the temperature-time passport of the A-band. The article provides data on the practical use of luminescence in the separation of diamond ores, provides some information on the design of separators. [ABSTRACT FROM AUTHOR]