Conventional robots are mainly made of rigid materials, such as steel and aluminum. Recently there has been a surge in the popularity of soft robots owing to their inherent compliance, strong adaptability and capability to work effectively in unstructured environments. Of the multitude of soft actuation technologies, dielectric elastomer actuators (DEAs), also nicknamed ‘artificial muscles’, exhibit fast response, large deformation and high energy density, and can simply be actuated with electric voltage. In this paper, we will discuss applications of DEAs to soft robots, including robotic grippers, terrestrial robots, underwater robots, aerial robots and humanoid robots. We will survey the state of the art regarding these interesting applications and outline the challenges and perspectives. As we know, there have been extensive studies on dielectric elastomer technology in the aspects of materials, mechanics, design, fabrication and controls. To enable practical applications, efforts are underway to decrease operational voltages, improve reliability, and impart new functionalities. Key challenges include the development of freestanding actuators, untethered operation, smart/electronics free actuators, solid and stretchable electrodes, miniaturization, combination of synergistic actuation technologies to impart novel functionalities, development of effective control strategies, etc. We hope that this review can facilitate and enhance applications of dielectric elastomer technology to soft robots.