Autonomous marine vehicles, which provide a platform for the successful implementation of special tasks, such as maritime rescue, maritime measurement, and dangerous goods monitoring, have been widely utilized. In the last decade, considerable attention has been paid to the analysis, modeling, and networked control of autonomous marine vehicles. This survey provides recent advances in networked and deep reinforcement learning-based control for autonomous marine vehicles. Typical mathematical models of autonomous marine vehicles are introduced first as the foundation for control of autonomous marine vehicles. Then, networked and deep reinforcement learning-based control for autonomous marine vehicles is reviewed. Finally, some challenges and open issues are presented to motivate the future research.