Episodic memory (memories of the personal past) and prospecting the future (anticipating events) are often described as mental time travel (MTT). While most use this description metaphorically, we argue that episodic memory may allow for MTT in at least some robust sense. While episodic memory experiences may not allow us to literally travel through time, they do afford genuine awareness of past-perceived events. This is in contrast to an alternative view on which episodic memory experiences present past-perceived events as mere intentional contents. Hence, episodic memory is a way of coming into experiential contact with, or being again aware of, what happened in the past. We argue that episodic memory experiences depend on a causal-informational link with the past events being remembered, and that, assuming direct realism about episodic memory experiences, this link suffices for genuine awareness. Since there is no such link in future prospection, a similar argument cannot be used to show that it also affords genuine awareness of future events. Constructivist views of memory might challenge the idea of memory as genuine awareness of remembered events. We explain how our view is consistent with both constructivist and anti-causalist conceptions of memory. There is still room for an interpretation of episodic memory as enabling genuine awareness of past events, even if it involves reconstruction.