This article quantifies the effects of increasing global geopolitical uncertainty on the size of migration flows to Western Europe. Uncertainty is measured by the number of victims of terrorist attacks worldwide. The effect on migration flows is quantified through the estimation of vector autoregressive models on a panel of 15 European countries and on France, thanks to an original migration dataset. The estimations suggest that the flows of permanent migrants are generally reduced by global terrorism. In particular, the increase in uncertainty that followed the attacks of September 11, 2001, caused an 8% drop in flows to Europe and a 19% drop in flows to France. The effect of global uncertainty on the flow of asylum seekers depends on the country: on average in Europe, asylum applications increase with terrorism, but for France, they decrease with terrorism. This difference can be explained by the geographical position and border control policies of France.