This article examines the nature and evolution of mental time travel. Evidence for capacities in other animals is reviewed and evaluated in terms of which components of the human faculty appear to be shared and which are unique. While some nonhuman animals store episodic memory traces and can display a range of future-directed capacities, they do not appear to share the open-ended ability to construct mental scenarios, to embed them into larger narratives, nor to reflect and communicate on what they entail. Nested scenario building and the urge to exchange mental experiences seem to set human minds apart in this context as in many others. The article ends with a discussion of the archeological evidence for mental time travel, focusing on deliberate practice as an example of its tremendous fitness consequences.