Abstract: Boundary layer transition prediction has always been a hot and difficult research topic in the field of fluid mechanics. Among them, the crossflow induced transition plays a crucial role in the transition phenomenon on the surface of the aircraft, which is affected by the freestream disturbance, wall surface roughness, wall pressure gradient, local sweep angle, crossflow characteristic Reynolds number, Mach number, wall curvature and temperature. All those factors make the prediction of the cross-flow transition very complicated and difficult. In recent years, many research institutions have proposed various prediction methods for this problem, which are basically divided into two categories: one is to establish the critical transition Reynolds number criterion, and to determine whether transition occurs; the other type is the modeled linear stability theory, which calculates the cross-flow disturbance amplification factor and compares it with the transition threshold to determine whether transition occurs. Several typical prediction models of crossflow dominated transition based on local variables of low-speed boundary layer and high-speed boundary will be systematically reviewed and summarized, and the future research directions will be prospected.