The cable-driven flexible manipulator has several advantages, such as high deformation, small mass, and low energy consumption. With the development of robotic applications, the precise modeling and effective control of cable-driven flexible manipulators have become a key research direction for domestic and foreign scholars. This study reviews cable-driven flexible manipulators′ modeling and control methods; analyzes their kinematic, dynamic, and static modeling from the modeling method; and summarizes the control methods from model-based and model-free perspectives. The model-based control methods are divided into kinematic and dynamic modeling. Meanwhile, the model-free control methods include fuzzy, neural network, adaptive, and sliding mode control. Finally, the future research direction of modeling and motion control of cable-driven flexible manipulators prospects.