The review considers the main approaches to the development of structural and active elements for actuators in soft robotics. An analysis of publications in the field of recent achievements in electroresponsive polymer materials operating on the principles of Maxwell pressure and electrostriction is provided. The main problems of the development of locomotor elements for soft robotics in terms of the design and structural analysis of actuators, and methods of activating the locomotor function, are noted. Moreover, some issues related to promising materials for soft robotics and methods for their production are considered. Great emphasis in the review is placed on an integrated approach and modern methods in the study of materials, including the use of mega-science facilities. Modern technological approaches to the design and manufacturing of soft-robotic devices are outlined. Appropriate analytical and numerical methods that allow relevant material models to be obtained for a comprehensive description of the behavior of actuators for soft robotics are considered. An overview of the functional prototypes of soft robots, designed according to the principle of nature-likeness, with active elements made of electroresponsive polymer materials is presented.