In all human cultures, people gesture iconically. However, the evolutionary basis of iconic gestures is unknown. In this study, chimpanzees and bonobos, and 2- and 3-year-old children, learned how to operate two apparatuses to get rewards. Then, at test, only a human adult had access to the apparatuses, and participants could instruct her about how to obtain the rewards. Children frequently produced appropriate iconic gestures, but with the exception of one human-raised chimpanzee, great apes did not gesture iconically. However, chimpanzees pointed to a reward outside the apparatus in another experimental condition, showing their motivation and ability to communicate with the human to request it. They also manipulated a duplicate apparatus in appropriate ways, though it was unclear if they did this to communicate with the human. Although great apes may have some of the prerequisite skills involved, iconic gestures come naturally to humans in a way that they do not for great apes.