Gallium oxide (Ga₂O₃) is an emerging wide bandgap semiconductor that has attracted a large amount of interest due to its ultra-large bandgap of 4.8 eV, a high breakdown field of 8 MV/cm, and high thermal stability. These properties enable Ga₂O₃ a promising material for a large range of applications, such as high power electronic devices and solar-blind ultraviolet (UV) photodetectors. In the past few years, a significant process has been made for the growth of high-quality bulk crystals and thin films and device optimizations for power electronics and solar blind UV detection. However, many challenges remain, including the difficulty in p-type doping, a large density of unintentional electron carriers and defects/impurities, and issues with the device process (contact, dielectrics, and surface passivation), and so on. The purpose of this article is to provide a timely review on the fundamental understanding of the semiconductor physics and chemistry of Ga₂O₃ in terms of electronic band structures, optical properties, and chemistry of defects and impurity doping. Recent progress and perspectives on epitaxial thin film growth, chemical and physical properties of defects and impurities, p-type doping, and ternary alloys with In₂O₃ and Al₂O₃ will be discussed.