A cable-driven parallel robot (CDPR) is a type of high-performance robot that integrates cable-driven kinematic chains and parallel mechanism theory. It inherits the high dynamics and heavy load capacities of the parallel mechanism and significantly improves the workspace, cost, and energy efficiency simultaneously. As a result, CDPRs have irreplaceable positions in industrial and technological fields, such as astronomy, aerospace, logistics, simulators, and rehabilitation. CDPRs follow the cutting-edge trend of rigid-flexible fusion, reflect advanced lightweight design concepts, and have become a frontier topic in robotics research. This paper summarizes the kernel theories and developments of CDPRs, covering configuration design, cable-force distribution, workspace and stiffness, performance evaluation, optimization, and motion control. Kinematic modeling, workspace analysis, and cable-force solution are illustrated. Stiffness and dynamic modeling and analysis methods are discussed. To further promote the development, researchers should strengthen the investigation in configuration innovation, rapid calculation of workspace, performance evaluation, stiffness control, and rigid-flexible coupling dynamics. In addition, engineering problems such as cable materials, reliability design, and a unified control framework require attention.