β-Ga2O3, with excellent bandgap, breakdown field, and thermal stability properties, is considered to be one of the most promising candidates for power devices including field-effect transistors (FETs) and for other applications such as Schottky barrier diodes (SBDs) and solar-blind ultraviolet photodetectors. Ohmic contact is one of the key steps in the β-Ga2O3 device fabrication process for power applications. Ohmic contact techniques have been developed in recent years, and they are summarized in this review. First, the basic theory of metal–semiconductor contact is introduced. After that, the representative literature related to Ohmic contact with β-Ga2O3 is summarized and analyzed, including the electrical properties, interface microstructure, Ohmic contact formation mechanism, and contact reliability. In addition, the promising alternative schemes, including novel annealing techniques and Au-free contact materials, which are compatible with the CMOS process, are discussed. This review will help our theoretical understanding of Ohmic contact in β-Ga2O3 devices as well as the development trends of Ohmic contact schemes.