Abstract: Numerical simulation is widely used in the vacuum flashover study of its mechanism and mitigation. We summarize and introduce the detailed physical processes, modeling algorithms, technical challenges, and corresponding solutions of vacuum flashover global model and numerical simulation, as well as their future development. The secondary electron emission avalanche theory, on which the vacuum flashover global model is based, is first introduced. The flashover development is divided into initiation from cathode triple junction, multipactor, outgassing from insulator surface, and final surface plasma discharge. Corresponding particle modeling technology, algorithm and recently obtained simulation results of each stage are reviewed. The physical processes, including cathode triple junction field emission, secondary electron emission from dielectric, transport of desorbed neutral, and electron-neutral collisions, are discussed. Subsequently, the methods for flashover mitigation based on the global model are reviewed, including field emission suppression via electric field optimization, mitigation of secondary electron emission avalanche by surface structures, and reduction of dielectric outgassing. The essential role of numerical simulation in vacuum flashover study is highlighted. Finally, non-particle flashover modeling approaches for separate flashover stages and their future prospects are discussed, including kinetic model, fluid model, hybrid model, and integrated model of above-surface and sub-surface processes.