Abstract: With the development of magnetic bearing technology, the rotor speed is getting higher and higher, and the subsequent stability issues are increasingly prominent. The research on the dynamics of flexible rotors with magnetic bearings has become the focus of the research. This paper summarized the theory and process of stability control of magnetic bearing-flexible rotor, including analysis methods and optimization methods, the unbalance vibration and multi frequency vibration. The development trends and key issues of the research on the dynamics of magnetic levitation bearings and flexible rotors were put forward, which provide a reference for the research of dynamics of magnetic levitation bearings and flexible rotors.