In our conventional experience, we experience ourselves as positioned in the present between an ever-receding past and an ever advancing present. The phenomenology of internal time has occupied sages and philosophers for centuries; advanced practitioners are said to experience the flow of time in a radically different way. From a neuroscientific perspective, our internal time line represents a significant computational challenge. How does our brain manage to construct a time line of past events, which are no longer present in the environment, and future events, which have not yet come to pass? To facilitate dialogue, we review a recent neurocognitive hypothesis for how an internal time line could be constructed. We compare the hypothesis to neurophysiological data from a variety of brain regions, and behavioral findings from a variety of fields of cognitive psychology.