Human social interactions are comprised of complex patterns of actions and reactions. In particular, eye gaze plays an important social role as it is indicative of an individual's focus of attention and can thus reveal important aspects of the individual's internal states to others. In this talk, we present data from several human-human and human-robot interaction studies that were specifically designed to probe the temporal dynamics of human eye gaze patterns in realistic social interaction tasks. The results show interesting similarities between human-human and human-robot conditions such as the temporal dynamics of attention distributions after onsets of movements by interactants, but also important differences in patterns of facial fixations or overall distributions of attention allocation.