The brain has finite processing resources so that, as tasks become harder, performance
degrades. Where do the limits on these resources come from? We focus on a variety of
capacity-limited buffers related to attention, recognition, and memory that we claim have a
two-dimensional ‘map’ architecture, where individual items compete for cortical real
estate. This competitive format leads to capacity limits that are flexible, set by the nature of the
content and their locations within an anatomically delimited space. We contrast this format with the
standard ‘slot’ architecture and its fixed capacity. Using visual spatial attention
and visual short-term memory as case studies, we suggest that competitive maps are a concrete and
plausible architecture that limits cognitive capacity across many domains.