International negotiations on climate change, along with recent upsurges in migration across the Mediterranean Sea, have highlighted the need to better understand the possible effects of climate change on human migration-in particular, across national borders. Here we examine how, in the recent past (2000-2014), weather variations in 103 source countries translated into asylum applications to the European Union, which averaged 351,000 per year in our sample. We find that temperatures that deviated from the moderate optimum (similar to 20 degrees C) increased asylum applications in a nonlinear fashion, which implies an accelerated increase under continued future warming. Holding everything else constant, asylum applications by the end of the century are predicted to increase, on average, by 28% (98,000 additional asylum applications per year) under representative concentration pathway (RCP) scenario 4.5 and by 188% (660,000 additional applications per year) under RCP 8.5 for the 21 climate models in the NASA Earth Exchange Global Daily Downscaled Projections (NEX-GDDP).