Grinding is an important method for precision machining and ultra-precision grinding. It is used to generate parts with high surface finish, high form accuracy and surface integrity. In recent years, grinding technology in precision machining and ultra-precision machining of ceramics, glass and high-strength alloys and other hard materials has been applied widely. Grinding process is complex, once known as "black processing technology." Computer simulation is an important method to research the grinding mechanism and optimize the grinding process parameters. Especially in recent years as the development of computer calculation speed, the improvement of computer graphics theory and the gradual maturity of artificial intelligence technology, experts and scholars whose research subject related grinding had done a lot of work on grinding simulation. This paper gives an overview of the current state of the art in simulation of grinding processes: Physical simulation (material removal mechanism, grinding force, grinding temperature, etc.) and geometrical simulation (surface topography and surface integrity) are taken into account, and outlined with respect to their achievements in this paper. Furthermore, the capabilities and the limitations of the presented simulation approaches will be exemplified.