Catastrophe theory is an important branch in the field of nonlinear science. As a mathematical tool, it is widely used in many fields, especially in the slope engineering. Firstly the development history and basic principle of catastrophe theory are briefly described in this paper, and then from three aspects the application and research progress of catastrophe theory in slope engineering are discussed, including the stability analysis of the slope based on cusp catastrophe method, the slope stability estimation based on catastrophe progression method and the cusp catastrophe prediction model for landslide time forecast based on gray theory and fuzzy mathematics. This paper focuses on the corresponding theoretical model, application method and effect, and discusses the development trend of catastrophe theory in slope engineering according to current problems in the end.