Due to its ultra-wide bandgap (6.2 eV), high thermal conductivity (340 W/(m·℃)), high breakdown field (11.7 MV/cm), excellent ultraviolet (UV) transparency and high chemical and thermal stabilities, bulk aluminum nitride (AlN) substrate is an excellent candidate for GaN-based high-temperature, high-frequency, high-power electronic and deep-UV optoelectronic devices with high Al content. The Physical Vapor Transport method (PVT) is the most promising technique for the growth of large-size and high-quality bulk AlN single crystals. The crystal structure, basic properties, growth theory and natural growth habits of AlN crystals grown by the PVT method are introduced primarily. Based on the PVT growth strategy of AlN single crystal, the research history of spontaneous growth, homoepitaxy and heteroepitaxy, the advantages and disadvantages of each growth strategy and the latest progress are reviewed in great detail. The recent progress and future challenges of AlN crystal growth by the PVT method are addressed as well.