This article reviews recent progress in the use of stimuli-responsive polymers for soft robotics. First, we introduce different types of representative stimuli-responsive polymers, which include liquid crystal polymers and elastomers, hydrogels, shape memory polymers, magnetic elastomers, electroactive polymers, and thermal expansion actuators. We focus on the mechanisms of actuation and the evaluation of performance and discuss strategies for improvements. We then present examples of soft robotic applications based on stimuli-responsive polymers for bending, grasping, walking, swimming, flying, and sensing control. Finally, we discuss current opportunities and challenges of stimuli-responsive soft robots for future study. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 5 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.