<p>This article provides a comprehensive exploration of the current research landscape in the field of soft actuation technology applied to bio-inspired soft robots. In sharp contrast to their conventional rigid counterparts, bio-inspired soft robots are primarily constructed from flexible materials, conferring upon them remarkable adaptability and flexibility to execute a multitude of tasks in complex environments. However, the classification of their driving technology poses a significant challenge owing to the diverse array of employed driving mechanisms and materials. Here, we classify several common soft actuation methods from the perspectives of the sources of motion in bio-inspired soft robots and their bio-inspired objects, effectively filling the classification system of soft robots, especially bio-inspired soft robots. Then, we summarize the driving principles and structures of various common driving methods from the perspective of bionics, and discuss the latest developments in the field of soft robot actuation from the perspective of driving modalities and methodologies. We then discuss the application directions of bio-inspired soft robots and the latest developments in each direction. Finally, after an in-depth review of various soft bio-inspired robot driving technologies in recent years, we summarize the issues and challenges encountered in the advancement of soft robot actuation technology.</p>