For scientists, explanations of natural phenomenon based on optimality principles are critical tools for understanding the phenomena that shape the solutions the brain devises for the complex perceptual and motor problems of daily life. The neuroscientist David Marr called this type of analysis the "computational approach''. While the computational approach has been applied with a great deal of success to phenomena such as neural coding and human motor control, the success of the computational approach for studying interactive behavior, particularly social behavior, has been more modest. The purpose of this dissertation is threefold: to make the case for the study of social interaction from the computational perspective; to understand the challenges involved in this study and provide computational tools to address these challenges; and to apply the computational approach to the study of social behavior in the real world. Our principle contributions are : (1) developing a framework for both analyzing and synthesizing behaviors in continuous state, action, and time from the perspective of the intentions that these behaviors appear to be realizing (our approach is well-suited for many motor-control and social-interaction problems), and (2) carrying out two computational studies of early infant social behavior that shed light on the computational forces that shape development. Our empirical results provide a new view of early infant social behavior as intentional, with the surprising intention of maximizing time spent with mother smiling at infant and the infant not smiling herself