People can time travel cognitively because they can remember events having occurred at particular times in the past (episodic memory) and because they can anticipate new events occurring at particular times in the future. The ability to assign points in time to events arises from human development of a sense of time and its accompanying time-keeping technology. The hypothesis is advanced that animals are cognitively stuck in time: that is, they have no sense of time and thus have no episodic memory or ability to anticipate long-range future events. Research on animals' abilities to detect time of day, track short time intervals, remember the order of a sequence of events, and anticipate future events are considered, and it is concluded that the stuck-in-time hypothesis is largely supported by the current evidence.