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Microgrid is becoming an attractive concept to meet the increasing demands for energy and deal with air pollutions. Distributed energy sources (DERs) in Microgrid are usually interfaced with the utility grid by inverters, so the characteristics of Microgrid stability are much different from that of a traditional grid. However, the classifications, guidelines, and analysis method of Microgrid stability are well behind of the Microgrid development. In this paper, a Microgrid stability classification methodology is proposed on the basis of the of Microgrid characteristics investigation, which considers the Microgrid operation mode, types of disturbance and time frame. Then a comprehensive review of the body of research on Microgrid stability is presented in order to identify and advance the field. Finally, some challenges and suggestions of Microgrid stability for further researches are discussed.