Mammals have evolved specialized brain systems to support efficient navigation within diverse habitats and over varied distances, but while navigational strategies and sensory mechanisms vary across species, core spatial components appear to be widely shared. This review presents common elements found in mammalian spatial mapping systems, focusing on the cells in the hippocampal formation representing orientational and locational spatial information, and 'core' mammalian hippocampal circuitry. Mammalian spatial mapping systems make use of both allothetic cues (space-defining cues in the external environment) and idiothetic cues (cues derived from self-motion). As examples of each cue type, we discuss: environmental boundaries, which control both orientational and locational neuronal activity and behaviour; and 'path integration', a process that allows the estimation of linear translation from velocity signals, thought to depend upon grid cells in the entorhinal cortex. Building cognitive maps entails sampling environments: we consider how the mapping system controls exploration to acquire spatial information, and how exploratory strategies may integrate idiothetic with allothetic information. We discuss how 'replay' may act to consolidate spatial maps, and simulate trajectories to aid navigational planning. Finally, we discuss grid cell models of vector navigation.