When we find our way in the environment, we need to integrate information about location, direction and distance into a coherent map-like representation. Our work over the last 10 years has suggested that the medial entorhinal cortex plays a central role in this process. A key component of the entorhinal network for spatial mapping is the grid cell, which we discovered, together with our colleagues, in 2005. Grid cells fire only when animals move through specific, regularly spaced positions. Their active firing positions form a hexagonal pattern that spans, for each cell, the entire local space available to the animal (Fig 1). The periodic pattern is reminiscent of the cross-points of graphic paper but the repeating units are equilateral triangles, not squares. Grid cells interact with other specialized cell types, such as head-direction cells and border cells. Head-direction cells signal orientation whereas border cells fire only near the edge of the local environment (Fig 2). Together, these entorhinal cells establish a coherent generic map of local space that is maintained across environments, independently of the animal's speed and direction and independently of the identity of the particular landmarks of the place. Figure 1 Entorhinal grid cell Figure 2 Border cells, grid cells and head direction cells are the elements of a metric representation of local space and are likely to be used when animals navigate through the environment »Grid cells have attracted attention because the crystal-like structure underlying their firing fields is not, like in sensory systems, imported from the outside world, but is created within the brain itself.« “One synapse” downstream, in the hippocampus, the map is associated with specific features and experiences, forming individualized maps that are stored in the neural networks of this brain region. Studies of grid cells may thus provide access to some of the basic computational operations of cortical circuits. In this Perspective, we shall review the work that led to the discovery of grid cells and the entorhinal spatial map, concluding with a brief look to the future.