In recent years, soft actuators composed of flexible materials, integrating various actuation methods, have found widespread application across multiple fields. Including, Deep-sea exploration, rehabilitation robots, etc.), These systems offer significant advantages over traditional rigid robots, particularly in terms of adaptability and safety in human–robot interaction. One key feature of soft robots is their actuation mechanisms, which enable precise control and enhanced adaptability to diverse environments. For instance, robots used in deep-sea exploration can utilize hydraulic actuation to mitigate challenges associated with electrical systems, such as water leakage, control box failure, and electrical short circuits. This paper primarily explores the principles and bioinspiration behind different soft robots, focusing on various actuation methods, including pneumatic actuation, shape memory alloys, Dielectric Elastomer Actuators (DEAs), Electroactive Polymers (EAPs), magnetic actuation, etc. while discussing their respective advantages and limitations. Additionally, it provides a comprehensive review of existing soft robots utilized in diverse applications. Finally, particular attention is given to the field of hand rehabilitation, a growing area of research due to the increasing number of patients suffering from motor dysfunction caused by stroke. We specifically review the current state of soft hand exoskeleton gloves, summarizing their development based on different actuation principles.