This paper surveys the recent advances in dynamic positioning (DP) control for marine crafts. DP of marine crafts means that a craft can maintain a fixed position and heading, or move along a predetermined trajectory slowly without the anchoring system, using only its own thruster system to counteract ocean disturbances. The survey is by no means exhaustive but provides a survey of some of the major technological advancements in DP controller design over the years of research and development. Firstly, the model of marine crafts and some difficult problems in DP control are introduced including the impact of multiple source disturbance, unavailable velocity measurement information, resource conservation and performance optimization, destabilizing impact of faults and network security and compound multi-constraint restrictions. Then, the DP control schemes in recent years are summarized and classified in detail. Finally, some theoretical and technical problems are proposed, including online data-driven model-free control, man–machine combination intelligent control and composite hierarchical anti-disturbance control to guide future investigations.