Chemically powered micro- and nanomotors are small devices that are self-propelled by catalytic reactions in fluids. Taking inspiration from biomotors, scientists are aiming to find the best architecture for self-propulsion, understand the mechanisms of motion, and develop accurate control over the motion. Remotely guided nanomotors can transport cargo to desired targets, drill into biomaterials, sense their environment, mix or pump fluids, and clean polluted water. This Review summarizes the major advances in the growing field of catalytic nanomotors, which started ten years ago.