Conventional silicon (Si)-based power devices face physical limitations—such as switching speed and energy efficiency—which can make it difficult to meet the increasing demand for high-power, low-loss, and fast-switching-frequency power devices in power electronic converter systems. Gallium nitride (GaN) is an excellent candidate for next-generation power devices, capable of improving the conversion efficiency of power systems owing to its wide band gap, high mobility, and high electric breakdown field. Apart from their cost effectiveness, GaN-based power high-electron-mobility transistors (HEMTs) on Si substrates exhibit excellent properties—such as low ON-resistance and fast switching—and are used primarily in power electronic applications in the fields of consumer electronics, new energy vehicles, and rail transit, amongst others. During the past decade, GaN-on-Si power HEMTs have made major breakthroughs in the development of GaN-based materials and device fabrication. However, the fabrication of GaN-based HEMTs on Si substrates faces various problems—for example, large lattice and thermal mismatches, as well as ‘melt-back etching’ at high temperatures between GaN and Si, and buffer/surface trapping induced leakage current and current collapse. These problems can lead to difficulties in both material growth and device fabrication. In this review, we focused on the current status and progress of GaN-on-Si power HEMTs in terms of both materials and devices. For the materials, we discuss the epitaxial growth of both a complete multilayer HEMT structure, and each functional layer of a HEMT structure on a Si substrate. For the devices, breakthroughs in critical fabrication technology and the related performances of GaN-based power HEMTs are discussed, and the latest development in GaN-based HEMTs are summarised. Based on recent progress, we speculate on the prospects for further development of GaN-based power HEMTs on Si. This review provides a comprehensive understanding of GaN-based HEMTs on Si, aiming to highlight its development in the fields of microelectronics and integrated circuit technology.