One of the grand challenges in neuroscience is to comprehend neural computation in the association cortices, the parts of the cortex that have shown the largest expansion and differentiation during mammalian evolution and that are thought to contribute profoundly to the emergence of advanced cognition in humans. In this Review, we use grid cells in the medial entorhinal cortex as a gateway to understand network computation at a stage of cortical processing in which firing patterns are shaped not primarily by incoming sensory signals but to a large extent by the intrinsic properties of the local circuit.