A dielectric elastomer actuated system is a novel flexible actuator based on the deformation property of dielectric material to actuate mechanical systems, and the use of a dielectric elastomer to actuate and control robots has become a current research hotspot in the field of soft robotics. Therefore, the core key issues of a dielectric elastomer drive system, namely, the modeling and control methods of the dielectric elastomer actuated system, are reviewed and presented in a comprehensive manner. Firstly, the structure and the actuating process of dielectric elastomer actuated systems are described, and the actuation principle of dielectric elastomer drive is explained in detail. Then, the complex nonlinear characteristics of dielectric elastomer actuated systems are reviewed in the aspects of modeling and control, with detailed analysis of the advantages and limitations of different modeling methods and control strategies. Finally, the issues in modeling and control of dielectric elastomers and future research progress are discussed.