Bio-inspired underwater robotics is emerging as a transformative technology, offering new ways to explore and monitor aquatic environments more efficiently and gently. Drawing inspiration from marine animals such as jellyfish, fish, crabs, and octopuses, these robots replicate natural movement patterns to achieve superior propulsion, agility, and the ability to switch between different modes of locomotion. Unlike conventional underwater vehicles, these soft and flexible designs allow for smoother navigation in complex environments. Recent progress in materials science, actuation technologies, and intelligent control systems has made these robots more adaptable and capable of functioning across varied underwater scenarios. This review provides a detailed look into the latest advancements in bio-inspired underwater robotics, highlighting essential design concepts, smart actuation methods, and control strategies that mimic the intelligence of natural organisms. It also explores their growing real-world applications, from delicate underwater inspections and marine research to complex search-and-rescue operations. By examining notable innovations such as jellyfish-inspired robots designed for energy-efficient movement and modular, magnetically actuated designs that can adapt to specific tasks, this paper showcases the field's dynamic progress. Ultimately, this paper aims at offering a clear understanding of current capabilities while identifying the key challenges and research gaps that must be addressed to bring these promising technologies into broader, practical use.