The primary task of marine surveillance is to construct a perfect marine situational awareness (MSA) system that serves to safeguard national maritime rights and interests and to maintain blue homeland security. Progress in maritime wireless communication, developments in artificial intelligence, and automation of marine turbines together imply that intelligent shipping is inevitable in future global shipping. Computer vision-based situational awareness provides visual semantic information to human beings that approximates eyesight, which makes it likely to be widely used in the field of intelligent marine transportation. We describe how we combined the visual perception tasks required for marine surveillance with those required for intelligent ship navigation to form a marine computer vision-based situational awareness complex and investigated the key technologies they have in common. Deep learning was a prerequisite activity. We summarize the progress made in four aspects of current research: full scene parsing of an image, target vessel re-identification, target vessel tracking, and multimodal data fusion with data from visual sensors. The paper gives a summary of research to date to provide background for this work and presents brief analyses of existing problems, outlines some state-of-the-art approaches, reviews available mainstream datasets, and indicates the likely direction of future research and development. As far as we know, this paper is the first review of research into the use of deep learning in situational awareness of the ocean surface. It provides a firm foundation for further investigation by researchers in related fields.