Innovation policy can be a crucial component of governments' responses to crises. Because speed is a paramount objective, crisis innovation may also require different policy tools than innovation policy in non-crisis times, raising distinct questions and tradeoffs. In this paper, we survey the U.S. policy response to two crises where innovation was crucial to a resolution: World War II and the COVID-19 pandemic. After providing an overview of the main elements of each of these efforts, we discuss how they compare, and to what degree their differences reflect the nature of the central innovation policy problems and the maturity of the U.S. innovation system. We then explore four key tradeoffs for crisis innovation policy---top-down vs. bottom-up priority setting, concentrated vs. distributed funding, patent policy, and managing disruptions to the innovation system---and provide a logic for policy choices. Finally, we describe the longer-run impacts of the World War II effort and use these lessons to speculate on the potential long-run effects of the COVID-19 crisis on innovation policy and the innovation system.