Episodic memory, enabling conscious recollection of past episodes, can be distinguished from semantic memory, which stores enduring facts about the world. Episodic memory shares a core neural network with the simulation of future episodes, enabling mental time travel into both the past and the future. The notion that there might be something distinctly human about mental time travel has provoked ingenious attempts to demonstrate episodic memory or future simulation in non-human animals, but we argue that they have not yet established a capacity comparable to the human faculty. The evolution of the capacity to simulate possible future events, based on episodic memory, enhanced fitness by enabling action in preparation of different possible scenarios that increased present or future survival and reproduction chances. Human language may have evolved in the first instance for the sharing of past and planned future events, and, indeed, fictional ones, further enhancing fitness in social settings.