Several types of neurons involved in spatial navigation and memory encode the distance and direction (that is, the vector) between an agent and items in its environment. Such vectorial information provides a powerful basis for spatial cognition by representing the geometric relationships between the self and the external world. Here, we review the explicit encoding of vectorial information by neurons in and around the hippocampal formation, far from the sensory periphery. The parahippocampal, retrosplenial and parietal cortices, as well as the hippocampal formation and striatum, provide a plethora of examples of vector coding at the single neuron level. We provide a functional taxonomy of cells with vectorial receptive fields as reported in experiments and proposed in theoretical work. The responses of these neurons may provide the fundamental neural basis for the (bottom-up) representation of environmental layout and (top-down) memoryguided generation of visuo-spatial imagery and navigational planning. [H1] Introduction Place cells fire whenever an animal traverses a specific location in an environment (the spatial receptive field [G] of that neuron, also known as its 'place field', FIG. 1a). Since the discovery of place cells in the rat hippocampus by O'Keefe and Dostrovsky 1 , researchers have uncovered a multitude of additional spatially-selective cell types in rodents: that is, neurons whose receptive fields reference some aspect of an organism's location, state of motion, pose or its relationship to environmental features (such as boundaries, landmarks and other objects). The spatial receptive fields of some of these cells correspond to vectors, indicating the distance and direction in space (relative to the animal's current location) within which the presence of an environmental feature will drive the neuron to fire. Such 'vectorial codes' for space have received comparatively less attention than the coding performed by place cells or other well-known spatially-selective cell types, such as grid cells [G] 2 (FIG. 1a) and head direction cells [G] 3,4. Vectorial codes for space are expressed by boundary vector cells 5,6 , border cells 7,8 , landmark vector cells 9 and object vector cells 10 in allocentric (that is, world-centered) coordinates. Just like place fields, the receptive fields of these vector-coding cells do not reflect the orientation of the animal but do rotate together with the prominent environmental features that control head direction cell firing 11. Egocentric counterparts of some of these cells-in which the direction of receptive fields are referenced relative to the facing direction of the agent-have also been found 12-15 , as well as cells that exhibit head direction-modulated boundary responses 16,17 .