People regularly travel through time mentally to remember and reconstruct past events and to anticipate and plan future events. We suggest that a bi-cone structure best describes human mental time travel (MTT) abilities. Experiments with scrub-jays, rats and non-human primates have investigated whether MTT is uniquely human by examining the abilities of these animals to remember what, where and when an event occurred and to anticipate future events. We argue that animal memory for when an event happened must be distinguished from memory for how long ago it happened to properly evaluate parallels with human capabilities. Similarly, tests of future MTT in animals must show that they are planning for a specific time in the future to demonstrate qualitative comparability with human MTT.