Electro-active polymers (EAP) are emerging as feasible materials to mimic muscle-like actuation. Among EAPs, dielectric elastomer (DE) devices are soft or flexible capacitors, composed of a thin elastomeric membrane sandwiched between two compliant electrodes, that are able to transduce electrical to mechanical energy, actuators, and vice versa, generators. Initial studies concentrated mainly on dielectric elastomer actuators (DEAs) and identified the electro-mechanical principles and material requirements for an optimal performance. Those requirements include the need for polymers with high dielectric permittivity and stretchability and low dielectric loss and viscoelastic damping. Hence, attaining elastomeric materials with those features is the focus of current research developments. This review provides a systematic overview of such research, highlighting the advances, challenges and future applications of DEAs.