We report on a new class of fast, high-curvature, low-voltage, reconfigurable, micrometer-scale shape-memory actuators. They bend to the smallest radius of curvature of any electrically controlled microactuator (~500 nanometers), are fast (<100-millisecond operation), and operate inside the electrochemical window of water. These shape-memory actuators can be used to create basic electrically reconfigurable microscale robot elements including actuating surfaces, origami-based three-dimensional shapes, morphing metamaterials, and mechanical memory elements.