Abstract: Aimed at understanding the modeling methods about the discharge physical process of ion thruster hollow cathode,various modeling methods were reviewed,including fluid models,Particle-in-Cell(PIC) models,hybrid models and reduced-order models.The physical models' characteristics,application areas and implementation outlines were analyzed,which would serve the modeling methods selection of hollow cathode modeling and simulation with theoretical basis.It would promote modeling solutions to the engineering problems that encountered in the development and experiment process.