The increasing frequency of extreme events, exogenous and endogenous, poses challenges for our societies. The current pandemic is a case in point; but once-in-a-century weather events are also becoming more common, leading to erosion, wildfire and even volcanic events that change ecosystems and disturbance regimes, threaten the sustainability of our life-support systems, and challenge the robustness and resilience of societies. Dealing with extremes will require new approaches and large-scale collective action. Preemptive measures can increase general resilience, a first line of protection, while more specific reactive responses are developed. Preemptive measures also can minimize the negative effects of events that cannot be avoided. In this paper, we first explore approaches to prevention, mitigation and adaptation, drawing inspiration from how evolutionary challenges have made biological systems robust and resilient, and from the general theory of complex adaptive systems. We argue further that proactive steps that go beyond will be necessary to reduce unacceptable consequences.