Humans and animals use mental representations of the spatial structure of the world to navigate. The classical view is that these representations take the form of Euclidean cognitive maps, but alternative theories suggest that they are cognitive graphs consisting of locations connected by paths. We review evidence suggesting that both map-like and graph-like representations exist in the mind/brain that rely on partially overlapping neural systems. Maps and graphs can operate simultaneously or separately, and they may be applied to both spatial and nonspatial knowledge. By providing structural frameworks for complex information, cognitive maps and cognitive graphs may provide fundamental organizing schemata that allow us to navigate in physical, social, and conceptual spaces. Spatial navigation has been suggested to rely either on Euclidean cognitive maps or on graph-like representations of routes between locations. Instead of being competing hypotheses, cognitive maps and cognitive graphs may coexist in the same individuals, with their availability and use depending on environmental characteristics and navigational demands. Cognitive maps and cognitive graphs are instantiated by partially distinct but partially overlapping neural systems in the hippocampal formation, frontal lobes, and scene-selective cortical regions. Both representational systems can likely support abstract thought; Euclidean maps are suited for representing content varying along continuous dimensions, whereas cognitive graphs are suited for representing state transitions and discrete associations between items. [ABSTRACT FROM AUTHOR]