This paper presents the origin, expression and principle of six traditional hysteretic nonlinear models, which are dry friction model, bilinear model, Davidenkov model, BoucWen model, trace method model and Bingham model, and analyzes their advantages, disadvantages and applications. In addition, some latest modified models are introduced and the corresponding investigations on these modified models are also presented. Finally, the status quo of hysteretic nonlinearity modeling is summarized and the research direction is predicted.