Currently, the useable compressive properties of a composite are restricted by set design limits well below the expected intrinsic performance of the materials contained within. The next generation of high-performance fibre-reinforced polymer composites will need to address the challenge of improving the absolute performance of composites in compression. This task requires a rethink of the whole system; not only to address practical limitations of current materials, but their combination, interface, and their architecture. The mechanisms involved do not simply act over the nano-, macro-, or meso-level independently, but are mutually related at the system level, complicating the approach.