We propose a computational model of the emergence of gaze following skills in infant-caregiver interactions. The model is based on the idea that infants learn that monitoring their caregiver's direction of gaze allows them to predict the locations of interesting objects or events in their environment (Moore & Corkum, 1994). Elaborating on this theory, we demonstrate that a specific Basic Set of structures and mechanisms is sufficient for gaze following to emerge. This Basic Set includes the infant's perceptual skills and preferences, habituation and reward-driven learning, and a structured social environment featuring a caregiver who tends to look at things the infant will find interesting. We review evidence that all elements of the Basic Set are established well before the relevant gaze following skills emerge. We evaluate the model in a series of simulations and show that it can account for typical development. We also demonstrate that plausible alterations of model parameters, motivated by findings on two different developmental disorders - autism and Williams syndrome - produce delays or deficits in the emergence of gaze following. The model makes a number of testable predictions. In addition, it opens a new perspective for theorizing about cross-species differences in gaze following.