Aluminum nitride (AlN) and gallium nitride (GaN) play an essential role in modern electronics, particularly in optoelectronics. Highly efficient light-emitting devices covering the ultraviolet to green spectral region are fabricated from these materials. Despite all efforts, the growth of large-size and high-quality AlN and GaN crystals for substrates, which are thermally and lattice-matched to the AlGaN-based device structures, is still in its infancy. This is due to the high equilibrium vapor pressure of nitrogen above these compounds, which requires growth techniques employing either the vapor phase or liquid solutions. The best commercially available GaN substrates show a high dislocation density of >105 per cm2 and strong bowing with a radius of curvature smaller than 10 m. This article reviews current growth techniques that look promising and may become commercially viable.