The advent of variable stiffness soft robotic grippers furnishes a conduit for exploration and manipulation within uncharted, non-structured environments. The paper provides a comprehensive review of the necessary technologies for the configuration design of soft robotic grippers with variable stiffness, serving as a reference for innovative gripper design. The design of variable stiffness soft robotic grippers typically encompasses the design of soft robotic grippers and variable stiffness modules.To adapt to unfamiliar environments and grasp unknown objects, a categorization and discussion have been undertaken based on the contact and motion manifestations between the gripper and the things across various dimensions: points contact (PC), lines contact (LC), surfaces contact (SC), and full-bodies contact (FBC), elucidating the advantages and characteristics of each gripping type. Furthermore, when designing soft robotic grippers, we must consider the effectiveness of object grasping methods but also the applicability of the actuation in the target environment. The actuation is the propelling force behind the gripping motion, holding utmost significance in shaping the structure of the gripper. Given the challenge of matching the actuation of robotic grippers with the target scenario, we reviewed the actuation of soft robotic grippers. We analyzed the strengths and limitations of various soft actuation, providing insights into the actuation design for soft robotic grippers. As a crucial technique for variable stiffness soft robotic grippers, variable stiffness technology can effectively address issues such as poor load-bearing capacity and instability caused by the softness of materials. Through a retrospective analysis of variable stiffness theory, we comprehensively introduce the development of variable stiffness theory in soft robotic grippers and showcase the application of variable stiffness grasping technology through specific case studies. Finally, we discuss the future prospects of variable stiffness grasping robots from several perspectives of applications and technologies.