In this paper, thermodynamical properties of AlN, GaN and InN are considered. It is shown that significant differences in melting conditions, thermal stability and solubilities in liquid group III metals lead to different possibilities of growing crystals from high temperature solutions, at Na pressure up to 20 kbar. It is shown that the best conditions for crystal growth at available pressure and temperature conditions can be achieved for GaN. High quality 6-10 mm single crystals of GaN have been grown at high N-2 pressure in 60-150 h processes. The mechanisms of nucleation and growth of GaN crystals are discussed on the basis of the experimental results. The crystallization of AlN is less efficient due to relatively low solubility of AlN in liquid Al. Possibility for the growth of InN crystals is strongly limited since this compound loses its stability at T > 600 degrees C, even at 2 GPa N-2 pressure. The crystals of GaN grown at high pressure are the first crystals of this material used for homoepitaxial layer deposition. Both MOCVD and MBE methods have been successfully applied. Structural, electrical and optical properties of both GaN single crystals and homoepitaxial layers are reviewed.