Catastrophe theory is a kind of mathematical method which aims to apply and interpret the discontinuous phenomenon. Since its emergence, it has been widely used to explain a variety of emergent phenomena in the fields of natural science, social science, management science and some other science and technology fields. Firstly, this paper introduces the theory of catastrophe in several aspects, such as its generation, radical principle, basic characteristics and development. Secondly, it summarizes the main applications of catastrophe theory in the field of mechanical engineering, focusing on the research progress of catastrophe theory in revealing catastrophe of rotor vibration state, analyzing friction and wear failure, predicting metal fracture, and so on. Finally, it advises that later development of catastrophe theory should pay more attention to the combination of itself with other traditional nonlinear theories and methods. This paper provides a beneficial reference to guide the application of catastrophe theory in mechanical engineering and related fields for later research.