Gaze following is the ability to redirect one’s gaze to the location where another agent is looking. We present a computational model of how human infants or other agents may acquire gaze following by learning to predict the locations of interesting sights from the looking behavior of other agents through reinforcement learning. The model accounts for many findings about the development of gaze follow- ing in human infants. During learning, the model develops pre-motor representations that exhibit many properties characteristic of mirror neurons, but they are specific to looking behaviors. The existence of such a new class of mirror neurons is the main prediction of our model. The model also offers a parsi- monious account of how these and possibly other mirror neurons may acquire their special response properties. In this account, visual representations of other agents’ actions become associated with pre- motor neurons that represent the intention to perform corresponding actions. The model also demon- strates how this development may be obstructed in autism spectrum disorder, giving rise to specific physiological and anatomical differences in the mirror system.