This article describes the challenges that victims, insurers and governments face in dealing with insurance for low-probability high-consequence events in both developed and developing economies. In developed economies, given their limited experience with catastrophes, there is a tendency for all three parties to engage in short-term intuitive thinking rather than long-term deliberative thinking when making insurance-related decisions. Here, public-private partnerships can encourage investment in protective measures prior to a disaster, deal with affordability problems and provide coverage for catastrophic risks. Insurance premiums based on risk provide signals to residents and business as to the hazards they face and enable insurers to lower premiums for properties where steps have been taken to reduce their risk. To address issues of equity and fairness, homeowners who cannot afford insurance could be given vouchers tied to loans for investing in loss reduction measures. The National Flood Insurance Program provides an opportunity to implement a public-private partnership that could eventually be extended to other extreme events, while the United Kingdom's Flood Re provides a good case study. In developing economies, insurance penetration is historically very low. This requires innovative solutions to catastrophic risk insurance such as risk pooling, parametric insurance and micro insurance. Nevertheless, the uninsured and uncompensated losses of disasters remain extensive, implying the need for public-private partnerships.