Dielectric elastomer actuators (DEAs) are flexible lightweight actuators that can generate strains of over 100 %. They are used in applications ranging from haptic feedback (mm-sized devices), to cm-scale soft robots, to meter-long blimps. DEAs consist of an electrode-elastomer-electrode stack, placed on a frame. Applying a voltage between the electrodes electrostatically compresses the elastomer, which deforms in-plane or out-of plane depending on design. Since the electrodes are bonded to the elastomer, they must reliably sustain repeated very large deformations while remaining conductive, and without significantly adding to the stiffness of the soft elastomer. The electrodes are required for electrostatic actuation, but also enable resistive and capacitive sensing of the strain, leading to self-sensing actuators. This review compares the different technologies used to make compliant electrodes for DEAs in terms of: impact on DEA device performance (speed, efficiency, maximum strain), manufacturability, miniaturization, the integration of self-sensing and self-switching, and compatibility with low-voltage operation. While graphite and carbon black have been the most widely used technique in research environments, alternative methods are emerging which combine compliance, conduction at over 100 % strain with better conductivity and/or ease of patternability, including microfabrication-based approaches for compliant metal thin-films, metal-polymer nano-composites, nanoparticle implantation, and reel-to-reel production of μm-scale patterned thin films on elastomers. Such electrodes are key to miniaturization, low-voltage operation, and widespread commercialization of DEAs.