The Inconel 625 (IN625) superalloy has a high strength, excellent fatigue, and creep resistance under high-temperature and high-pressure conditions, and is one of the critical materials used for manufacturing high-temperature bearing parts of aeroengines. However, the poor workability of IN625 alloy prevents IN625 superalloy to be used in wider applications, especially in applications requiring high geometrical complexity. Laser powder bed fusion (LPBF) is a powerful additive manufacturing process which can produce metal parts with high geometrical complexity and freedom. This paper reviews the studies that have been done on LPBF of IN625 focusing on the microstructure, mechanical properties, the development of residual stresses, and the mechanism of defect formation. Mechanical properties such as microhardness, tensile properties, and fatigue properties reported by different researchers are systematically summarized and analyzed. Finally, the remaining issues and suggestions on future research on LPBF of IN625 alloy parts are put forward.