Abstract: In this paper, we review the development process of researches on laws of seismic dynamic response, analyze the rhythmic characteristics of dynamic response of slope on its cross section and describe the dynamic instability mechanism. We summarize the methods of dynamic stability analysis that are scattered in a large number of relevant literatures, classify them by research methods and analysis principle, and point out their advantages and disadvantages. On this basis, we summarize a series of issues that exist in the current study on seismic dynamic response of slope, point out the significance of forming an evaluation system of dynamic stability of slope by seismic action parameters and indicate the direction of future research.