Fruit and vegetable picking grippers are important technology to achieve rapid and labor-saving harvest. However, most of the existing fruit and vegetable picking grippers still use traditional rigid or underactuated grippers, which often cause fruits and vegetables damage by the heavy mass and lack of high-precision control, and have poor compliance in the operation process. In recent years, inspired by soft creature’s tentacles, soft robotic grippers have appeared and been used in robotics due to the emergence of soft robots. Soft robotic gripper, which is made of flexible material, is a new type of gripper for general purposes with grasping and holding capabilities enabled by a simple control scheme. Under the infinite degrees of freedom, the soft robotic gripper can change its shape and size corresponding to the load in a large range. These advantages overcome the defects of traditional fruit and vegetable picking robots, such as rigidity and poor adaptability. Moreover, soft robotic gripper is easy to manufacture and can be integrated with manual operation without any large-scale safe requirement. This paper gives a research on limitations of the traditional grippers and summarizes the characteristics of ideal picking grippers of fruit and vegetable. In addition, the concept of soft robotic grippers is introduced in detail, and the current development status about soft robotic grippers is described. The manuscript also summarizes the progress and superiority of soft robotic grippers in fruit and vegetable picking as well as strong adaptability to the environment. The characteristics of the soft robotic grippers driven by the common driving mode including pneumatic, cable, shape memory alloy and electroactive polymer mode have been analyzed in the process of fruit and vegetable grasping and picking. Compared with the rigid grippers, in addition to the simple control and mechanism, the soft robotic grippers have high-degree flexibility, adaptability and versatility. Based on the related work, the problems of modeling and control of fruit and vegetable picking devices have been discussed, and possible solutions of soft robotic grippers are also summarized by means of analysis and classification. We can choose the appropriate control methods according to the surface characteristics of picked fruits and vegetables. Finally, we conclude that multi-sensing, variable stiffness, multi-functional composite materials, as well as control strategies of fusion intelligence will be future development directions of fruit and vegetable picking grippers with the progress of micro-sensors and biomaterials. This research will provide theoretical and technical guidance for the development of fruit and vegetable picking grippers. It is expected that more fruit and vegetable picking operations could be carried out by soft robotic grippers, and the application will effectively reduce the damage rate of fruit and vegetable picking. As a new-generation operating device, the soft robotic grippers involve the development of materials, chemistry, machinery and other multidiscipline. Further studies are required to improve its design, controllability, manipulating methods, and so on. [ABSTRACT FROM AUTHOR]