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The transfer of organic carbon from the upper to the deep ocean by particulate export flux is the starting point for the long-term storage of photosynthetically fixed carbon. This ‘biological carbon pump’ is a critical component of the global carbon cycle, reducing atmospheric CO₂ levels by ~200 ppm relative to a world without export flux. This carbon flux also fuels the productivity of the mesopelagic zone, including important fisheries. Here we show that, despite its importance for understanding future ocean carbon cycling, Earth system models disagree on the projected response of the global export flux to climate change, with estimates ranging from −41% to +1.8%. Fundamental constraints to understanding export flux arise because a myriad of interconnected processes make the biological carbon pump challenging to both observe and model. Our synthesis prioritizes the processes likely to be most important to …