First, what is computed by the hippocampus is considered. Based on the effects of damage to the hippocampus and neuronal activity recorded in the primate hippocampus, it is suggested that it is involved in associating together information usually originating from different cortical regions, for example, about objects and their place in a spatial environment. The rapid formation of such context-dependent memories is prototypical of memories of particular events or episodes. Second, a computational theory of how it performs this function, based on neuroanatomical and neurophysiological information about the different neuronal systems contained within the hippocampus, is described. Key hypotheses are that the CA3 pyramidal cells operate as a single autoassociation network to store new episodic information as it arrives via a number of specialized preprocessing stages from many different association areas of the cerebral cortex, and that the dentate granule cell/mossy fiber system is important particularly during learning to help to produce a new pattern of firing in the CA3 cells for each episode. The computational analysis shows how many memories could be stored in the hippocampus, and how quickly the CA3 autoassociation system would operate during recall. The analysis is then extended to show how the CA3 system could be used to recall the whole of an episodic memory when only a fragment of it is presented. It is shown how this retrieval within the hippocampus could lead to recall of neuronal activity in association areas of the cerebral neocortex similar to that present during the original episode, via modified synapses in backprojection pathways from the hippocampus to the cerebral neocortex. The recalled information in the cerebral neocortex could then by used by the neocortex in the formation of long-term memories and/or in the selection of appropriate actions.