When Zika virus (ZIKV) emerged in the Americas, little was known about its biology, pathogenesis, and transmission potential, and the scope of the epidemic was largely hidden, owing to generally mild infections and no established surveillance systems. Surges in congenital defects and Guillain-Barré syndrome alerted the world to the danger of ZIKV. In the context of limited data, quantitative models were critical in reducing uncertainties and guiding the global ZIKV response. Here, we review some of the models used to assess the risk of ZIKV-associated severe outcomes, the potential speed and size of ZIKV epidemics, and the geographic distribution of ZIKV risk. These models provide important insights and highlight significant unresolved questions related to ZIKV and other emerging pathogens.