This article focuses on the neural and cognitive processes that support imagining or simulating future events, a topic that has recently emerged in the forefront of cognitive neuroscience. We begin by considering concepts of simulation from a number of areas of psychology and cognitive neuroscience in order to place our use of the term in a broader context. We then review neuroimaging, neuropsychological, and cognitive studies that have examined future-event simulation and its relation to episodic memory. This research supports the idea that simulating possible future events depends on much of the same neural machinery, referred to here as a core network, as does remembering past events. After discussing several theoretical accounts of the data, we consider applications of work on episodic simulation for research concerning clinical populations suffering from anxiety or depression. Finally, we consider other aspects of future-oriented thinking that we think are related to episodic simulation, including planning, prediction, and remembering intentions. These processes together comprise what we have termed “the prospective brain,” whose primary function is to use past experiences to anticipate future events.