Flight delays caused by thunderstorms are a significant and growing problem for airlines and the flying public. Thunderstorms disrupt the structured, preplanned flight routing and control process that is used to handle dense air traffic streams in congested airspace. Today's coping strategies are developed by traffic flow management (TFM) specialists who interpret weather measurements and forecasts to develop delay and rerouting strategies. The effectiveness of these strategies is limited by the lack of quantitative models for the capacity impacts of thunderstorms, and by the difficulty of developing and executing timely response strategies during rapidly changing convective weather. In this article, we describe initial work to develop more effective response strategies. We first review insights gained during operational testing of a simple but highly effective Route Availability Planning Tool that can significantly reduce convective-weather induced departure delays at congested airports. We then discuss work to develop core technical capabilities and applications that address broader TFM problems, including en route congestion. Objective models for airspace capacity reductions caused by thunderstorms are discussed, as is an associated scheduling algorithm that exploits the capacity estimates to develop broad-area TFM strategies that minimize delay. We conclude by discussing candidate real-time applications and airspace system performance analysis that is enabled by our weather-capacity models and optimal scheduling algorithm.