Biodegradable soft robots have been proposed for a variety of intelligent applications in soft robotics, flexible electronics, and bionics. Biodegradability offers an extraordinary functional advantage to soft robots for operations accompanying smart shape transformation in response to external stimuli such as heat, pH, and light. This review primarily surveyed the current advanced scientific and engineering strategies for integrating biodegradable materials within stimuli-responsive soft robots. It also focused on the fabrication methodologies of multiscale biodegradable soft robots, and highlighted the role of biodegradable soft robots in enhancing the multifunctional properties of drug delivery capsules, biopsy tools, smart actuators, and sensors. Lastly, the current challenges and perspectives on the future development of intelligent soft robots for operation in real environments were discussed.