Modular reconfigurable robots have rapidly become the frontier and hotspot in the field of robotics research in recent years due to their variable configurations and rich motion forms, which can perform tasks in unstructured or unknown environments. Modular robots have broad application prospects in military, medical, education, and many other engineering fields, with their typical representatives including bionic multi-legged modular robots, modular reconfigurable manipulators, lattice form modular robots, etc. The rich configuration design, diverse connection features, and expanding application scope of modular reconfigurable robots have brought many challenges and opportunities to dynamic modeling and control. This paper first expounds research background and significance of modular reconfigurable robots and outlines the configuration classification, configuration descriptions, and kinematic modeling methods. Following this, latest progress in the research of modular reconfigurable robot dynamics is systematically reviewed, including (1) overall system dynamic modeling, (2) dynamic modeling of joint surface and docking mechanism, and (3) control methods based on dynamic models. Finally, several open problems are presented for future studies.