Biomimetic stimuli-responsive materials can respond to various external stimuli in the form of structural or morphological transformations by actively or passively converting input energy into mechanical energy. They are the core element of soft actuators for typical smart devices like soft robots, artificial muscles, intelligent sensors and nanogenerators. While significant progresses have been made in bioinspired stimuli-responsive materials, they have not yet achieved the remarkable properties in biological systems. In this review, we will discuss recent advances in biomimetic stimuli-responsive materials that are instrumental for soft actuators. Different stimuli-responsive principles for soft actuators are firstly discussed, including fluidic, electrical, thermal, magnetic, light and chemical stimuli. We further summarize the state-of-the-art stimuli-responsive materials for soft actuators and explore the advantages and disadvantages of using electroactive polymers, magnetic soft composites, hydrogels, liquid crystal elastomers, shape memory alloys and chemical-responsive materials. Finally, we provide a critical outlook on the field of stimuli-responsive soft actuators, and emphasize the challenges in the process of their implementation to various industries.