The detection of elusive particles and in general the construction of detectors with high sensitivity for applications in the physics of rare events requires the use of new high quality crystals with enhanced characteristics. The production of such materials often depends upon the application of dedicated methods for the entire production process from synthesis of raw materials up to the storage and transport of the finished product ready for use for the construction of the particle detector. Cryogenic bolometers and the more sophisticated scintillating bolometers are among the most promising detectors used in rare event physics, particularly in Neutrinoless Double Beta Decay (0νDBD) experiments. Operated at extremely low temperatures (≈10mK) such devices need high purity crystals with a very high crystal perfection and low level of intrinsic radioactivity. Moreover, in the case of 0νDBD application, the crystal requires the presence of the nuclide of interest in a sufficient amount i.e. isotope enriched materials are employed. The current work reviews scientific and technological aspects related to the crystal production for rare events physics experiments, particularly for bolometric application. In the case of enriched isotopes used in 0νDBD experiments, the problems related to a maximum production yield are stressed. The discussion is illustrated with results obtained in the activities connected to the procurement of ZnSe crystals for the experiment Low-background Underground Cryogenic Installation For Elusive Rates (LUCIFER).