Abstract: Rotor system is the core component of rotating machinery, widely used in gas turbine engines, turbofan engines, compressors and machine tool spindles. The rotor system generally contained rotating parts and supporting parts. Supporting components are important load-carrying structure in the rotor system. The internal incentives that can be generated by the coupling of nonlinear factors such as geometric nonlinearity, rotor friction and connection nonlinearity from rotor system and nonlinearity of the support, made the dynamic behavior complex and occur chaos phenomena. Survey the research background and significance of the combined support-rotor system, outline the combined support scheme of support-rotor system and application in aero engine. Afterwards, systematically reviews recent advances in the five types of combined support-rotor system and the modeling methods, reduction method applied in high dimensional nonlinear dynamics of combined supported rotor system, as well as the calculation method of nonlinear dynamic differential equation. Finally, future noteworthy problems in the combined support-rotor system dynamic analysis are discussed.