As a physical quantity comprehensively describing the properties of fluid dynamic and thermodynamic, the potential vorticity receives widespread attention of meteorologists.Potential vorticity inversion theory has become one of the most important methods in typhoon research.In this paper, the advancement about the research of potential vorticity inversion theory in recent decades is briefly reviewed.The advancement about the application of potential vorticity inversion theory in typhoon research is summarized.We also discuss the possible problems relating to potential vorticity inversion theory.The methods for calculating the average potential vorticity state, the role of surface friction and the condition for balance may affect the inversion.Finally, some possible applications of potential vorticity inversion theory are predicted.