Cable-driven parallel robots (CDPRs) are categorized as a type of parallel manipulators. In CDPRs, flexible cables are used to take the place of rigid links. The particular property of cables provides CDPRs several advantages, including larger workspaces, higher payload-to-weight ratio and lower manufacturing costs rather than rigid-link robots. In this paper, the history of the development of CDPRs is introduced and several successful latest application cases of CDPRs are presented. The theory development of CDPRs is introduced focusing on design, performance analysis and control theory. Research on CDPRs gains wide attention and is highly motivated by the modern engineering demand for large load capacity and workspace. A number of exciting advances in CDPRs are summarized in this paper since it is proposed in the 1980s, which points to a fruitful future both in theory and application. In order to meet the increasing requirements of robot in different areas, future steps foresee more in-depth research and extension applications of CDPRs including intelligent control, composite materials, integrated and reconfigurable design.