We study time-critical search, where users have urgent information needs in the context of an acute problem. As examples, users may need to know how to stem a severe bleed, help a baby who is choking on a foreign object, or respond to an epileptic seizure. While time-critical situations and actions have been studied in the realm of decision-support systems, little has been done with time-critical search and retrieval, and little direct support is offered by search systems. Critical challenges with time-critical search include accurately inferring when users have urgent needs and providing relevant information that can be understood and acted upon quickly. We leverage surveys and search log data from a large mobile search provider to (a) characterize the use of search engines for time-critical situations, and (b) develop predictive models to accurately predict urgent information needs, given a query and a diverse set of features spanning topical, temporal, behavioral, and geospatial attributes. The methods and findings highlight opportunities for extending search and retrieval to consider the urgency of queries.