In this paper we discuss some literature relating to episodic memory, future episodic thinking and mental time travel in humans and non-human animals. We discuss the concept of mental time travel and argue that the concept relies on subjective phenomena such as consciousness and on this basis is not useful when studying episodic memory and future episodic thinking, particularly in non-human animals. We discuss recent work which emphasizes views of both episodic memory and future thinking which do not rely on such mental time travel and, more importantly, give less prominence to the concept of time. The implications of such a view for research into future thinking in non-human animals are considered.