The ability to construct a hypothetical situation in one's imagination prior to it actually occurring may afford greater accuracy in predicting its eventual outcome. The recollection of past experiences is also considered to be a reconstructive process with memories recreated from their component parts. Construction, therefore, plays a critical role in allowing us to plan for the future and remember the past. Conceptually, construction can be broken down into a number of constituent processes although little is known about their neural correlates. Moreover, it has been suggested that some of these processes may be shared by a number of other cognitive functions including spatial navigation and imagination. Recently, novel paradigms have been developed that allow for the isolation and characterization of these underlying processes and their associated neuroanatomy. Here, we selectively review this fast-growing literature and consider some implications for remembering the past and predicting the future.