This paper proposes the modeling and tracking control methods for the dielectric elastomer actuator (DEA). A dynamic model of the DEA is built, which is composed of an asymmetric hysteresis model, a creep model and a linear system. To compensate the hysteresis and creep nonlinearities of the DEA, an inverse compensation feedforward controller (ICFC) is designed based on the creep model and the inverse of the asymmetric hysteresis model. Besides, an extended state observer (ESO) is designed to estimate the unmeasurable state of the DEA, as well as uncertainties including the modeling errors, parameter perturbations and external disturbances. Then, a sliding mode feedback controller (SMFC) is designed cooperating with the ICFC to realize the high precision tracking control of the DEA. The convergence of the ESO and the whole control system are proved through the Lyapunov method. Finally, some experiments are executed to verify the effectiveness of the proposed modeling and control methods.