The dynamics of the magnetorheological damper is complex, including the inherent hysteresis characteristics and nonlinear creep behavior in the low-velocity region. Mathematical models for these complex dynamics are very important to the function of the damper. In this paper, a comparative study of the four parametric dynamic models, which are the hysteresis bi–viscous model, viscoelastic-plastic model, Bouc–Wen model, and improved Bouc–Wen model, is performed. The study includes the building of a common test apparatus and the parameter identification for the four models. The comparison of the four models concludes that (1) all four models are comparative and that (2) the improved Bouc–Wen model has the highest accuracy.