Cumulative cultural learning has been argued to rely on high-fidelity copying of other individuals’ actions. Iconic gestures of actions have no physical effect on objects in the world but merely represent actions that would have an effect. Learning from iconic gestures thus requires paying close attention to the teacher’s precise bodily movements—a prerequisite for high-fidelity copying. In three studies, we investigated whether 2- and 3-year-old children (N = 122) and great apes (N = 36) learn novel skills from iconic gestures. When faced with a novel apparatus, participants watched an experimenter perform either an iconic gesture depicting the action necessary to open the apparatus or a gesture depicting a different action. Children, but not great apes, profited from iconic gestures, with older children doing so to a larger extent. These results suggest that high-fidelity copying abilities are firmly in place in humans by at least 3 years of age.