In order to achieve the national strategic goals of peaking carbon emissions by 2030 and achieving carbon neutrality by 2060, the electricity-energy-ecosystem is undergoing significant transformation, presenting new opportunities for the development of new energy generation technologies. With the widespread adoption of renewable energy sources, such as solar and wind energy, microgrids have begun to play a prominent role as small-scale power systems. Microgrids, as small, autonomous power systems, have received significant attention in recent years. Microgrids can enhance energy sustainability by integrating renewable energy resources and energy storage systems, while also providing the capability to maintain power supply during main grid failures or planned maintenance. This article aims to review the advances in control strategy research for microgrid islanding operation, with a focus on the classification of control strategies, design principles, and their impact on microgrid stability. The article also explores potential directions for future research to enhance the efficiency and reliability of microgrid islanding operation, providing valuable references for future studies.