This article presents a comprehensive survey of reconfigurable modular robots, which covers the origin, history, the state of the art, key technologies, challenges, and applications of reconfigurable modular robots. An elaborative classification of typical reconfigurable modular robots is proposed based on the characteristics of the modules and the reconfiguration mechanism. As the system characteristics of reconfigurable modular robots are mainly dependent on the functions of modules, the mechanical and electrical design features of modules of typical reconfigurable modular robots are discussed in detail. Furthermore, an in-depth comparison analysis is conducted, which encompasses discussions of module shape, module degrees of freedom, module attribute, connection mechanisms, interface autonomy, locomotion modes, and workspace. Meanwhile, many reconfigurable modular robot researches focus on the study of self-X capabilities (i.e. self-reconfiguration, self-assembly, self-adaption, etc.), which embodies autonomy performance of reconfigurable modular robots in certain extent. An evolutionary cobweb evaluation model is proposed in this article to evaluate the autonomy level of reconfigurable modular robots. Although various reconfigurable modular robots have been developed and some of them have been put into practical applications such as search and rescue missions, there still exist many open theoretical, technical, and practical challenges in this field. This work is hopefully to offer a reference for the further developments of reconfigurable modular robots.