Wherever a loose bed of sand is subject to sufficiently strong winds, aeolian dunes form at wavelengths and growth rates that are well predicted by linear stability theory 1-3 . As dunes mature and coarsen, however, their growth trajectories become more idiosyncratic; nonlinear effects 1 , sediment supply 4 , wind variability 5 and geologic constraints 6, 7 become increasingly relevant, resulting in complex and history-dependent dune amalgamations. Here we examine a fundamental question: do aeolian dunes stop growing and, if so, what determines their ultimate size? Earth's major sand seas are populated by giant sand dunes, evolved over tens of thousands of years 8,9 . We perform a global analysis of the topography of these giant dunes, and their associated atmospheric forcings and geologic constraints, and we perform numerical experiments to gain insight on temporal evolution of dune growth. We find no evidence of a previously proposed limit to dune size by atmospheric boundary layer height 10 . Rather, our findings indicate that dunes may grow indefinitely in principle; but growth slows with increasing size, and may ultimately be limited by sand supply. We also demonstrate that giant dune size depends on both wind climate and sand supply through their control on dune morphology, revealing a topographic signature of geologic and climatic forcing in Earth's sand seas.