Powerful, centralized states controlling a large share of national income only begin to appear in Europe after 1500. We build a model that explains their emergence in response to the increasing importance of money for military success. When fiscal resources are not crucial for winning wars, the threat of external conflict stifles state-building. As finance becomes critical, internally cohesive states invest in state capacity while divided states rationally drop out of the competition, causing divergence. We emphasize the role of the "Military Revolution", a sequence of technological innovations that transformed armed conflict. Using data from 374 battles, we investigate empirically both the importance of money for military success and patterns of state-building in early modern Europe. The evidence is consistent with the predictions of our model.