Due to the unavailability of GPS signal, it is more urgent to develop the autonomous navigation capability for the underwater vehicles. In this paper, we summarize the development status of underwater SLAM (simultaneous localization and mapping) system. Different from the terrestrial or aerial SLAM that largely depends on the optical sensors, the underwater SLAM system mainly uses the acoustic sensors, i.e., sonars, to watch the environment. With respect to the general SLAM system, which is mainly composed of the front-end local dataassociation and the back-end global error adjustment, we briefly survey recent progress in sonar image registration and the loop closure detection. Furthermore, some heuristic problems are posed in the conclusion.