Existing soft actuators have persistent challenges that restrain the potential of soft robotics, highlighting a need for soft transducers that are powerful, high-speed, efficient, and robust. We describe a class of soft actuators, termed hydraulically amplified self-healing electrostatic (HASEL) actuators, which harness a mechanism that couples electrostatic and hydraulic forces to achieve a variety of actuation modes. We introduce prototypical designs of HASEL actuators and demonstrate their robust, muscle-like performance as well as their ability to repeatedly self-heal after dielectric breakdown-all using widely available materials and common fabrication techniques. A soft gripper handling delicate objects and a self-sensing artificial muscle powering a robotic arm illustrate the wide potential of HASEL actuators for next-generation soft robotic devices.