【Objective】Deformable Mirror(DM) is a key device in adaptive optics system for wavefront correction, and its performance directly determines the wavefront correction capability of the system. By studying DM and their control algorithm, the wavefront correction capability of adaptive optics system can be continuously improved. On one hand, the accuracy and response speed of DM can be enhanced to better correct various complex wavefront distortions. On the other hand, the control algorithm can be improved to increase the efficiency and accuracy of the correction. These studies will directly affect the imaging quality and performance of adaptive optics system. Therefore, investigating the DM and their control algorithm is of great significance for improving the wavefront correction capability, expanding application fields, and enhancing imaging quality and performance of adaptive optics system.【Methods】The article aims to summarize the research progress on DM and their control algorithm both domestically and int