Planetary gear systems have many advantages over other gear systems. Previous studies on its dynamic characteristics mostly used Earth as the reference system, which is inconsistent with the actual working conditions of many planetary gear systems, such as aircraft maneuvering, vehicle movement changes, etc. By analyzing representative research papers, this study summarizes the lumped-parameter, finite element, and rigid–flexible coupling models commonly used in studying the traditional dynamic characteristics. Then, the research status of gear–rotor and planetary gear systems in inertial and non-inertial systems is summarized. The research progress of load characteristics, vibration characteristics, and vibration control of the traditional planetary gear system is summarized. Finally, some suggestions for future development are put forward. There are a few studies on the non-inertial dynamics of planetary gear systems. The three analysis models have distinct characteristics and applications but can all be used in non-inertial systems. The dynamic analysis method of non-inertial rotor systems can be combined with the dynamic study of gear systems. It is of practical significance to study the non-inertial dynamic characteristics of planetary gear systems. Scholars can refer to the non-inertial dynamic research of the gear–rotor system, select the analysis model according to the needs, and continue to study the dynamic characteristics of the planetary gear system under the non-inertial system.