In recent years, significant advancements have been made in robotics, especially with the introduction of continuum and hyper-redundant robots. These robots can be highly flexible and manoeuvrable, which makes them suitable for intricate underwater maintenance, exploration, and inspection tasks. Inspired by the motions of aquatic life, underwater snake-like robots offer a good way to accomplish subsea maintenance, exploration, and inspection activities. While many studies have been conducted on hyper-redundant, snake-like robotic arms for maintenance and inspection in land-based applications, not as much about robotics intended for marine or underwater applications has been studied. This review critically examines recent advancements in the design, actuation, and modelling of these robotic systems, categorising them into two primary families: untethered mobile robots and tethered robotic manipulators. Key insights include the identification of strengths and limitations associated with various designs and actuation strategies, such as the high manoeuvrability but limited speed of bioinspired swimming robots compared to thruster-driven designs, and the complexity versus precision trade-offs inherent in tendon-driven manipulator arms. Furthermore, the modelling techniques employed across categories are systematically analysed, as well as challenges such as the modelling of fluid–structure interactions and the need for improved real-time models for compliant and soft robots.