Within the next several years, there will be a high level of autonomous technology that will be available for widespread use, which will reduce labor costs, increase safety, save energy, enable difficult unmanned tasks in harsh environments, and eliminate human error. Compared to software development for other autonomous vehicles, maritime software development, especially on aging but still functional fleets, is described as being in a very early and emerging phase. This introduces very large challenges and opportunities for researchers and engineers to develop maritime autonomous systems. Recent progress in sensor and communication technology has introduced the use of autonomous surface vehicles (ASVs) in applications such as coastline surveillance, oceanographic observation, multivehicle cooperation, and search and rescue missions. Advanced artificial intelligence technology, especially deep learning (DL) methods that conduct nonlinear mapping with self-learning representations, has brought the concept of full autonomy one step closer to reality. This paper surveys the existing work regarding the implementation of DL methods in ASV-related fields. First, the scope of this work is described after reviewing surveys on ASV developments and technologies, which draws attention to the research gap between DL and maritime operations. Then, DL-based navigation, guidance, control (NGC) systems and cooperative operations, are presented. Finally, this survey is completed by highlighting the current challenges and future research directions.