The aims of the paper are to update Rolls’ quantitative computational theory of hippocampal function and the predictions it makes about the different subregions (dentate gyrus, CA3 and CA1), and to examine behavioral and electrophysiological data that address the functions of the hippocampus and particularly its subregions. Based on the computational proposal that the dentate gyrus produces sparse representations by competitive learning and via the mossy fiber pathway forces new representations on the CA3 during learning (encoding), it has been shown behaviorally that the dentate gyrus supports spatial pattern separation during learning. Based on the computational proposal that CA3–CA3 autoassociative networks are important for episodic memory, it has been shown behaviorally that the CA3 supports spatial rapid one-trial learning, learning of arbitrary associations where space is a component, pattern completion, spatial short-term memory, and spatial sequence learning by associations formed between successive items. The concept that the CA1 recodes information from CA3 and sets up associatively learned backprojections to neocortex to allow subsequent retrieval of information to neocortex, is consistent with findings on consolidation. Behaviorally, the CA1 is implicated in processing temporal information as shown by investigations requiring temporal order pattern separation and associations across time; and computationally this could involve associations in CA1 between object and timing information that have their origins in the lateral and medial entorhinal cortex respectively. The perforant path input from the entorhinal cortex to DG is implicated in learning, to CA3 in retrieval from CA3, and to CA1 in retrieval after longer time intervals (“intermediate-term memory”) and in the temporal sequence memory for objects.