Drawing on studies of humans, rodents, birds and arthropods, I show that 'cognitive maps' have been used to describe a wide variety of spatial concepts. There are, however, two main definitions. One, sensu Tolman, O'Keefe and Nadel, is that a cognitive map is a powerful memory of landmarks which allows novel short-cutting to occur. The other, sensu Gallistel, is that a cognitive map is any representation of space held by an animal. Other definitions with quite different meanings are also summarised. I argue that no animal has been conclusively shown to have a cognitive map, sensu Tolman, O'Keefe and Nadel, because simpler explanations of the crucial novel short-cutting results are invariably possible. Owing to the repeated inability of experimenters to eliminate these simpler explanations over at least 15 years, and the confusion caused by the numerous contradictory definitions of a cognitive map, I argue that the cognitive map is no longer a useful hypothesis for elucidating the spatial behaviour of animals and that use of the term should be avoided.