Purpose: To conduct a survey on the research and development of cable-driven rehabilitation devices (CDRDs). Method: This review searches in the databases of PubMed, IEEE Xplore Digital Library, Science Direct, and Google Scholar using various combinations of the following keywords: cable, wire, rehabilitation, assistance, therapy, training, robot, elastic, and pneumatic. Searches in the above databases for references cited by the above-searched references are also conducted to include a larger context of CDRDs. Results: CDRDs are classified into four categories, namely, serial exoskeleton-based, parallel exoskeleton-based, serial end-effector-based, and parallel end-effector-based CDRDs. Each category of CDRDs are further grouped based on the part of the human body to be rehabilitated. All four categories of CDRDs are examined and compared and their advantages and shortcomings are discussed based on popular rehabilitation requirements on weight, adaptability, versatility, misalignment, and safety. Open issues of CDRDs are also discussed. Conclusions: Each category of CDRDs has its own advantages and shortcomings. The selection of a CDRD highly depends on the specific application. Regarding the convenience of setting up a CDRD for rehabilitation, parallel CDRDs usually have better adaptability than serial ones. However, uncertainties come with parallel CDRDs, which makes the control of parallel CDRDs more challenging. Moreover, the strategy of inherent safety has a great potential to further improve the safety of CDRDs.