At present, with the development of waterborne transport vehicles, research on ship faces a new round of challenges in terms of intelligence and autonomy. The concept of maritime autonomous surface ships (MASS) has been put forward by the International Maritime Organization in 2017, in which MASS become the new focus of the waterborne transportation industry. This paper elaborates on the state-of-the-art research on motion control of MASS. Firstly, the characteristics and current research status of unmanned surface vessels in MASS and conventional ships are summarized, and the system composition of MASS is analyzed. In order to better realize the self-adaptability of the MASS motion control, the theory and algorithm of ship motion control-related systems are emphatically analyzed under the condition of classifying ship motion control. Especially, the application of intelligent algorithms in the ship control field is summarized and analyzed. Finally, this paper summarizes the challenges faced by MASS in the model establishment, motion control algorithms, and real ship experiments, and proposes the composition of MASS motion control system based on variable autonomous control strategy. Future researches on the accuracy and diversity of developments and applications to MASS motion control are suggested.