The ability to find one's way depends on a widespread brain network of hippocampal and neocortical areas interfaced by the medial entorhinal cortex (MEC). Based on high-density recordings from individual cells in the MEC of freely moving rats, I will suggest that the MEC contains part of the brain's own coordinate system, a two-dimensional metric map representing the animal's changing location in the environment. A key component of this map is the 'grid' cell. Grid cells fire selectively at regularly spaced positions in the environment such that, for each cell, activity is observed at regularly spaced positions, almost like the cross points of graph paper, but with an equilateral triangle as the unit of the grid. In contrast to the multiple environment-specific representations coded by place cells downstream in the hippocampus, local ensembles of grid cells maintain a constant phase structure across environments, allowing position to be represented and updated by the same translation mechanism in all environments encountered by the animal. I will conclude by showing that the nature of hippocampal population responses is determined by coordinate shifts in the entorhinal spatial representation. Such coordinate shifts determine a fundamental property of hippocampal neuronal networks, namely pattern separation, or their ability to increase differences between overlapping input patterns before information is stored. The study of neuronal mechanisms of spatial representation and encoding in the entorhinal cortex and hippocampus will ultimately benefit the development of tools for the diagnosis and treatment of Alzheimer's disease, which commonly begins in just the brain area that contains the grid cells.