The current status of GaN crystal growth using the Sublimation Sandwich Technique is discussed in the paper. We use modeling to analyze gas dynamics in the reactor and the supply of the main gaseous species into the growth cell under growth conditions used in experiments. Important features of growth process — non-equilibrium cracking of ammonia, partial sticking of ammonia at the growing surface and kinetic limitation of GaN thermal decomposition — are taken into account in the model. Growth is carried out on sapphire and 6H-SiC substrates in ammonia atmosphere using a Ga/GaN mixture as the group-III element source. Single crystals of GaN of size 15×15 mm and up to 0.5 mm thick are normally grown with the optimized growth rates of 0.25-0.35 mm/h. The GaN crystals are characterized by photoluminescence, by the Color Cathodoluminescence Scanning Electron Microscopy technique, by differential double-crystal and triple-crystal X-ray diffractometry, and by electron paramagnetic resonance. Mechanisms of sublimation growth of GaN and physical limitations of the growth process are discussed.