Abstract: Microgrids have attracted widely attention due to its high proportion of renewable energy sources, high proportion of power electronic equipment and its flexible and controllable characteristics. However, microgrids are characterized by low inertia and weak damping because they convert energy through power electronic converters and do not have the inertia support provided by synchronous generators in traditional power grids. Therefore, the stability problem caused by the lack of inertia and damping of microgrid system is particularly prominent. Firstly, the problems caused by the lack of inertia and damping in microgrids and the interaction mechanism with frequency stability were described. Then, various control technologies based on inertia and damping simulation were summarized, such as virtual synchronous generator, virtual inertia adaptive control, generalized droop control and so on. And the research status of frequency stability and oscillation suppression strategy of AC microgrids and voltage stability of DC microgrids were summarized respectively. Finally, the future research and development direction was prospected from different operating scenarios, different load types and instability mechanism of microgrids.