When thinking about the future or the upcoming actions of another person, we mentally project ourselves into that alternative situation. Accumulating data suggest that envisioning the future (prospection), remembering the past, conceiving the viewpoint of others (theory of mind) and possibly some forms of navigation reflect the workings of the same core brain network. These abilities emerge at a similar age and share a common functional anatomy that includes frontal and medial temporal systems that are traditionally associated with planning, episodic memory and default (passive) cognitive states. We speculate that these abilities, most often studied as distinct, rely on a common set of processes by which past experiences are used adaptively to imagine perspectives and events beyond those that emerge from the immediate environment.