The increasing complexity of marine operations has intensified the need for intelligent robotic systems to support ocean observation, exploration, and resource management. Underwater swarm robotics offers a promising framework that extends the capabilities of individual autonomous platforms through collective coordination. Inspired by natural systems, such as fish schools and insect colonies, bio-inspired swarm approaches enable distributed decision-making, adaptability, and resilience under challenging marine conditions. Yet research in this field remains fragmented, with limited integration across algorithmic, communication, and hardware design perspectives. This review synthesises bio-inspired coordination mechanisms, communication strategies, and system design considerations for underwater swarm robotics. It examines key marine-specific algorithms, including the Artificial Fish Swarm Algorithm, Whale Optimisation Algorithm, Coral Reef Optimisation, and Marine Predators Algorithm, highlighting their applications in formation control, task allocation, and environmental interaction. The review also analyses communication constraints unique to the underwater domain and emerging acoustic, optical, and hybrid solutions that support cooperative operation. Additionally, it examines hardware and system design advances that enhance system efficiency and scalability. A multi-dimensional classification framework evaluates existing approaches across communication dependency, environmental adaptability, energy efficiency, and swarm scalability. Through this integrated analysis, the review unifies bio-inspired coordination algorithms, communication modalities, and system design approaches. It also identifies converging trends, key challenges, and future research directions for real-world deployment of underwater swarm systems.