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  1. Soft robotics represents a new set of technologies aimed at operating in natural environments and near the human body. To interact with their environment, soft robots require artificial muscles to actuate movement. These artificial muscles need to be as strong, fast, and robust as their natural counterparts. Dielectric elastomer actuators (DEAs) are promising soft transducers, but typically exhibit low output forces and low energy densities when used without rigid supports. Here, we report a soft composite DEA made of strain-stiffening elastomers and carbon nanotube electrodes, which demonstrates a peak energy density of 19.8 J/kg. The result is close to the upper limit for natural muscle (0.4–40 J/kg), making these DEAs the highest-performance electrically driven soft artificial muscles demonstrated to date. To obtain high forces and displacements, we used low-density, ultrathin carbon nanotube electrodes which can sustain applied electric fields upward of 100 V/μm without suffering from dielectric breakdown. Potential applications include prosthetics, surgical robots, and wearable devices, as well as soft robots capable of locomotion and manipulation in natural or human-centric environments.