Mental time travel is considered as the human ability to mentally travel backward or forward in time, re-experiencing past events, as well as imagining possible future ones. Episodic memory is defined as the recall of personally experienced events specifically referring to contextual information about what, where and when a particular event occurred. Source memory is another important aspect of episodic memory as it allows us to differentiate one episodic memory from another. It includes features (e.g. perceptual, contextual, temporal features) that were present when the episodic memory was formed. Futur planning is described as the ability of humans to flexibly anticipate their own mental states of need and act now to secure them. Some authors have stated that episodic memory has evolved to serve future planning. However, most hypotheses have been stated by considering results of research in vertebrates. This makes evolutionary hypotheses difficult to test as their complex cognitive abilities may have evolved from common ancestors. It appears now necessary to use a more inclusive, comparative framework to better understand the Evolution of complex cognition. Since the intelligence of modern cephalopod molluscs (e.g. cuttlefish and octopuses) has arisen independently of the vertebrate lineage, they appear to be highly promising species to study mental time travels from evolutionary, mechanistic, functional and comparative perspectives.