The motion planning and control method of automated vehicles, as the key technology of automated vehicles, directly affects the safety, comfort, and other technical indicators of vehicles. The planning module is responsible for generating a vehicle driving path. The control module is responsible for driving the vehicle. In this study, we review the main methods and achievements in motion planning and motion control for automated vehicles. The advantages and disadvantages of various planning and control methods are comparatively analyzed. Finally, some predictions and summaries based on the existing research results and trends are proposed. Through this analysis, it is believed that various types of algorithms will be further integrated in the future to complement each other’s strengths and weaknesses. The next area of research will be to establish more accurate vehicle models to describe vehicle motion, improve the generalization-solving ability of algorithms, and enhance the planning and control of integrated ‘human-vehicle-road’ traffic systems.