The robotic soft gripper is a significant and expanding area of study. It is primarily a unique gadget that interacts with the external environment in a certain actuating mode by utilizing the properties of flexible materials and biological shape design. Robotic grippers are increasingly needed in the fields of medical operations, auxiliary maintenance, land rescue, underwater grasping, and space manipulation due to the increasing demand for automation. However, conventional rigid gripper is not the ideal option or optimal design for particular activities requiring a high degree of adaptation and interaction. The soft gripper can interact with its surroundings safely and flexibly because it is comprised of flexible materials. Currently, certain technical system has been developed through research on flexible grippers, but it is still in its infancy. This paper reviews the materials and manufacturing technology, actuating technology, and sensing and control technology of flexible mechanical grippers. Finally, several main application areas of soft grippers are discussed from a technical point of view, as well as possible challenges for further development.