Self-governing small regions of power systems, known as "microgrids", are enabling the integration of small-scale renewable energy sources (RESs) while improving the reliability and energy efficiency of the electricity network. Microgrids can be primarily classified into three types based on their voltage characteristics and system architecture; 1) AC microgrids, 2) DC microgrids, and 3) Hybrid AC/DC microgrids. This paper presents a comprehensive review of stability, control, power management and fault ride-through (FRT) strategies for the AC, DC, and hybrid AC/DC microgrids. This paper also classifies microgrids in terms of their intended application and summarises the operation requirements stipulated in standards (e.g., IEEE Std. 1547. The control strategies for each microgrid architecture are reviewed in terms of their operating principle and performance. In terms of the hybrid AC/DC microgrids, specific control aspects, such as mode transition and coordinated control between multiple interlinking converters (ILCs) and energy storage system (ESS) are analysed. A case study is also presented on the dynamic performance of a hybrid AC/DC microgrid under different control strategies and dynamic loads. Hybrid AC/DC microgrids shown to have more advantages in terms of economy and efficiency compared with the other microgrid architectures. This review shows that hierarchical control schemes, such as primary, secondary, and tertiary control are very popular among all three microgrid types. It is shown that the hybrid AC/DC microgrids require more complex control strategies for power management and control compared to AC or DC microgrids due to their dependency on the ILC controls and the operation mode of the hybrid AC/DC microgrid. Case study illustrated the significant effects of microgrid feeder characteristics on the dynamic performance of the hybrid AC/DC microgrid. It is also revealed that any transient conditions either in the AC or DC microgrids could propagate through the ILC affecting the entire microgrid dynamic performance. Additionally, the critical control issues and the future research challenges of microgrids are also discussed in this paper.INDEX TERMS Energy storage system (ESS), hybrid AC/DC microgrid, IEEE Std. 1547-2018, interlinking converter (ILC), microgrid stability, power management, renewable energy sources (RESs).