Imagination is a biological function that is vital to human experience and advanced cognition. Despite this importance, it remains unknown how imagination is realized in the brain. Substantial research focusing on the hippocampus, a brain structure traditionally linked to memory, indicates that firing patterns in spatially tuned neurons can represent previous and upcoming paths in space. This work has generally been interpreted under standard views that the hippocampus implements cognitive abilities primarily related to actual experience, whether in the past (e.g. recollection, consolidation), present (e.g. spatial mapping) or future (e.g. planning). However, relatively recent findings in rodents identify robust patterns of hippocampal firing corresponding to a variety of alternatives to actual experience, in many cases without overt reference to the past, present or future. Given these findings, and others on hippocampal contributions to human imagination, we suggest that a fundamental function of the hippocampus is to generate a wealth of hypothetical experiences and thoughts. Under this view, traditional accounts of hippocampal function in episodic memory and spatial navigation can be understood as particular applications of a more general system for imagination. This view also suggests that the hippocampus contributes to a wider range of cognitive abilities than previously thought. This article is part of the theme issue 'Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.