Underwater surveillance has traditionally been carried out by means of surface and undersea manned vessels equipped with advanced sensor systems. This approach is often costly and manpower intensive. Marine robotics is an emerging technological area that enables the development of advanced networks for underwater surveillance applications. In contrast with the use of standard assets, these advanced networks are typically composed of small, low-power, and possibly mobile robots, which have limited endurance, processing and wireless communication capabilities. When deployed in a region of interest, these robots can cooperatively form an intelligent network achieving high performance with significant features of scalability, adaptability, robustness, persistence and reliability. Such networks of robots can be the enabling technology for a wide range of applications in the maritime domain. However, they also introduce new challenges for underwater distributed sensing, data processing and analysis, autonomy and communications. The main thrust of this study is to review the underwater surveillance scenario within a framework of four research areas: (i) underwater robotics, (ii) acoustic signal processing, (iii) tracking and distributed information fusion, and (iv) underwater communications networks. Progress in each of these areas as well as future challenges is presented.