Insects perform feats of strength and endurance that belie their small stature. Insect-scale robots-although subject to the same scaling laws-demonstrate reduced performance because existing microactuator technologies are driven by low-energy density power sources and produce small forces and/or displacements. The use of high-energy density chemical fuels to power small, soft actuators represents a possible solution. We demonstrate a 325-milligram soft combustion microactuator that can achieve displacements of 140%, operate at frequencies >100 hertz, and generate forces >9.5 newtons. With these actuators, we powered an insect-scale quadrupedal robot, which demonstrated a variety of gait patterns, directional control, and a payload capacity 22 times its body weight. These features enabled locomotion through uneven terrain and over obstacles.