Improving our ability to cope with large risks is one of the key challenges for humankind in this century. This article outlines a research program in this perspective. Starting with a concrete example of a relatively small disaster, it questions simplistic ideas of rationality. It then proposes a fresh look at the concepts of probability and utility in the context of socioecological systems. This leads first to an emphasis on the problem of equilibrium selection, and then to a distinction between three kinds of resilience that matter both for theory and practice of risk management. They can be investigated by paying attention to the transitions into and out of actual disasters.