We want to build robots capable of rich social interactions with humans, including natural communication and cooperation. This work explores how imitation as a social learning and teaching process may be applied to building socially intelligent robots, and summarizes our progress toward building a robot capable of learning how to imitate facial expressions from simple imitative games played with a human, using biologically inspired mechanisms. It is possible for the robot to bootstrap from this imitative ability to infer the affective reaction of the human with whom it interacts and then use this affective assessment to guide its subsequent behavior. Our approach is heavily influenced by the ways human infants learn to communicate with their caregivers and come to understand the actions and expressive behavior of others in intentional and motivational terms. Specifically, our approach is guided by the hypothesis that imitative interactions between infant and caregiver, starting with facial mimicry, are a significant stepping-stone to developing appropriate social behavior, to predicting others' actions, and ultimately to understanding people as social beings.