Recent evidence suggests that grid cell-like mechanisms may be present in the neocortex. In this paper we propose that cells that behave similar to grid cells exist in every cortical column and play an essential role in all cortical function. We present a theoretical framework for understanding how the neocortex operates based on cortical grid cells. Grid cells in the medial entorhinal cortex represent the location of an animal in various environments. We propose that cortical grid cells, in the lower layers of the neocortex, also represent a location. Whereas grid cells in the entorhinal cortex represent the location of one thing, the body, grid cells in the cortex simultaneously represent the location of hundreds of things. Cortical columns that receive input from different parts of the body track the location of each body part relative to external reference frames. Similarly, cortical columns that receive input from the retina track the location of visual features relative to external reference frames. Including a representation of location in each column provides a framework for understanding how the cortex learns the structure and behavior of objects (“what” regions) and how the cortex maps the space around our bodies (“where” regions). The similarity of circuitry observed in all cortical regions suggests that even high-level concepts are learned and represented in a location-based framework. Cortical grid cells suggest a new way of thinking about cortical function, one that is based on the interplay of sensory input and location processing. In this paper we describe this idea and explore some of its implications.