Vortex pump is a kind of non-clogging pump, which will cause a large amount of vortex during transportation. Four kinds of mathematical model of vortex pump are introduced with continuous improvement. Moreover, the internal flow state, calculation and design method are also presented. In addition, the influent of slurry and structure parameters is introduced. After analyzed above, the design method of vortex pump can be further investigated specific to different concentration, viscosity and particle sizes under different specific speed. The focus of future research is testing internal flow by the advanced technology, building up a new flow model and proposing complete and practical calculation method.