Abstract: Modular reconfigurable underwater robots (MRURs) have attracted increasing attention due to their potential to overcome the limitations of conventional underwater robots with fixed structures and single-task capabilities. This review summarizes recent progress in MRUR from three perspectives: modular structural design, sensing and perception, and control strategies. For structural design, this review examines module division, housing, and connectors, highlighting composite pressure-resistant structures and magnetic docking mechanisms as feasible solutions. For perception, MRURs require not only multisensor fusion but also topology awareness, docking perception, and distributed perception to handle changes in reconfiguration. For control, MRUR reconfiguration alters topology, dynamics and actuation; therefore, key issues include topology recognition, docking and separation control, propulsion redundancy, distributed coordination, and the transition toward self-reconfiguration. Finally, representative application scenarios, key technical challenges, and future research directions of MRURs are discussed. With continued technological progress, MRURs are expected to evolve toward self-reconfiguration and self-adaptation, achieving intelligent control and cooperative autonomy.