Ultrawide bandgap (UWBG) semiconductor materials, with bandgaps far wider than the 3.4 eV of GaN, have attracted great attention recently. As a typical representative, wurtzite aluminum nitride (AlN) material has many advantages including high electron mobility, high breakdown voltage, high piezoelectric coefficient, high thermal conductivity, high hardness, high corrosion resistance, high chemical and thermal stability, high bulk acoustic wave velocity, prominent second-order optical nonlinearity, as well as excellent UV transparency. Therefore, it has wide application prospects in next-generation power electronic devices, energy-harvesting devices, acoustic devices, optical frequency comb, light-emitting diodes, photodetectors, and laser diodes. Due to the lack of low-cost, large-size, and high-ultraviolet-transparency native AlN substrate, however, heteroepitaxial AlN film grown on sapphire substrate is usually adopted to fabricate various devices. To realize high-performance AlN-based devices, we must first know how to obtain high-crystalline-quality and controllable AlN/sapphire templates. This review systematically summarizes the recent advances in fabricating wurtzite AlN film on (0001)-plane sapphire substrate. First, we discuss the control principles of AlN polarity, which greatly affects the surface morphology and crystalline quality of AlN, as well as the electronic and optoelectronic properties of AlN-based devices. Then, we introduce how to control threading dislocations and strain. The physical thoughts of some inspirational growth techniques are discussed in detail, and the threading dislocation density (TDD) values of AlN/sapphire grown by various growth techniques are compiled. We also introduce how to achieve high thermal conductivities in AlN films, which are comparable with those in bulk AlN. Finally, we summarize the future challenge of AlN films acting as templates and semiconductors. Due to the fast development of growth techniques and equipment, as well as the superior material properties, AlN will have wider industrial applications in the future.