Although a definition of the imagination remains elusive, this appears to be a fundamental element of the human mind and seems most likely to be woven into our biological constitution. As such, an understanding of imagination requires an evolutionary perspective. Some aspects of imagination can be readily explained, notably that of imagining alternative future worlds when decisions need to be made as to how to act. But many aspects of imagination, especially those that involve fantasy, are more difficult to explain from an evolutionary point of view. The paper tackles this issue and examines the course of human evolution, seeking to establish what types of imagination were present in a range of human ancestors and relatives between the time of the common ancestor of modern humans and the great apes at 5 mya, and emergence of the Upper Palaeolithic.