One of the most notable ecological trends—described more than 2,300 years ago by Theophrastus—is the association of small leaves with dry and cold climates, which has recently been recognized for eudicotyledonous plants at a global scale. For eudicotyledons, this pattern has been attributed to the fact that small leaves have a thinner boundary layer that helps to avoid extreme leaf temperatures and their leaf development results in vein traits that improve water transport under cold or dry climates. However, the global distribution of leaf size and its adaptive basis have not been tested in the grasses, which represent a diverse lineage that is distinct in leaf morphology and that contributes 33% of terrestrial primary productivity (including the bulk of crop production). Here we demonstrate that grasses have shorter and narrower leaves under colder and drier climates worldwide. We show that small grass leaves have thermal advantages and vein development that contrast with those of eudicotyledons, but that also explain the abundance of small leaves in cold and dry climates. The worldwide distribution of leaf size in grasses exemplifies how biophysical and developmental processes result in convergence across major lineages in adaptation to climate globally, and highlights the importance of leaf size and venation architecture for grass performance in past, present and future ecosystems.