Cable-driven parallel robots have become a hot research topic in the field of robotics in recent years due to the characteristics of simple structure, small motion inertia, reconfigurability, and fast response speed, etc. The cable-driven flexible manipulator provides a certain adaptability and softness for operation due to the flexibility and elasticity of driving cable, and consequently it can achieve good dynamic interaction between the operating objects and the manipulators, and improve the ability to prevent broken loss coupling, which has also attracted widespread attention from researchers in the field of agricultural robotics. Due to the working environment of agricultural picking robots has the characteristics of unstructured and uncertainty, and most of the fruit outer skin is fragile and easy to damage, the requirements for picking robots that come into directly contacted with the fruits are stricter, ensuring stable grasping without damaging the fruits. In order to achieve efficient and precise operations of picking robots, lightweight and flexible end execution agencies that interact with biological friendly interaction are key theoretical technologies that urgently need to be broken through. This article first elaborates on the characteristics and development overview of cable-driven flexible manipulators with commercial application prospects. Then, the research progress of the theory such as the design, modeling and control of cable-driven flexible robotics at home and abroad is reviewed in detail. Further the typical application development of cable-driven flexible robots in the field of physical rehabilitation and dexterous grabbing is outlined. A detailed analysis is conducted on the significance of the application of cable-driven flexible manipulators in the field of agricultural picking, and the current research status of cable-driven flexible manipulators in tomato picking, apple picking, strawberry picking, and blackberry picking. Aiming at the problems of low picking accuracy, poor versatility, high cost, damage and low picking efficiency of cable-driven flexible manipulator in agricultural picking at the present stage, it is pointed out that in the future, the commercialization of cable-driven flexible manipulator needs to make innovations in agricultural machinery and agronomy collaboration, modular and reconfigurable design, improving interaction safety, multi-sensor integration, picking sequence planning and strong robust control in this study and it provides new ideas and methods for the design of mechanized non-destructive picking mechanisms for fruits and vegetables.