Spatial navigation can serve as a model system in cognitive neuroscience, in which specific neural representations, learning rules, and control strategies can be inferred from the vast experimental literature that exists across many species, including humans. Here, we review this literature, focusing on the contributions of hippocampal and striatal systems, and attempt to outline a minimal cognitive architecture that is consistent with the experimental literature and that synthesizes previous related computational modeling. The resulting architecture includes striatal reinforcement learning based on egocentric representations of sensory states and actions, incidental Hebbian association of sensory information with allocentric state representations in the hippocampus, and arbitration of the outputs of both systems based on confidence/uncertainty in medial prefrontal cortex. We discuss the relationship between this architecture and learning in model-free and model-based systems, episodic memory, imagery, and planning, including some open questions and directions for further experiments. Chersi and Burgess review the neural mechanisms of spatial navigation in rodents and humans to extract a common “cognitive architecture,” identifying the learning rules and representations at work in hippocampal, striatal, and parietal systems and discussing remaining open questions.