As for other catastrophic risks, insurers must charge a premium that may be several times higher than the annual expected losses in order to meet their solvency constraints. In addition, some of the potential losses are not insurable or difficult to be covered by insurance (to date). Insurers are reluctant in particular to provide coverage for loss of life or personal injury occurring between ten and thirty years after the nuclear accident occurred, while only some would refuse full coverage for costs of measures of reinstatement for impaired environment or for cost of preventive measures. Beyond a certain level, the state is the sole entity able to bear the accident risk, and socialisation of such residual risk is the most efficient economic solution. As seen in this chapter, any estimate of the expected frequency and costs from a severe nuclear accident is extremely challenging and highly controversial. The major difficulty would therefore be to provide a valid estimate of the risk from a nuclear accident and of the residual risk that is borne by the state.