Satellite-to-ground laser communication (SGL) can address the spectrum limitation of traditional microwave communication and satisfy the increasing communication demand of satellite ground links. The adaptive optics (AO) system is an integral part of SGL, and it can effectively suppress the impacts of atmospheric turbulence and improve link stability and reliability. This paper introduces typical optical ground-station AO systems at home and abroad and its primary parameters. Based on the research results of AO in laser communication, the development trend followed by the AO system, including its improved wavefront detection ability, enhanced correction capability, stabilized and reliable operating performance, and improved automatic operation, is summarized. This study provides a reference for AO system development in SGL to ensure better availability of SGL link.