Several issues relating to insurance and the damage costs of climate change are discussed. It is argued that the option of insuring climate change is severely limited because the associated damages are hardly quantifiable and little diversifiable; in addition, binding contracts are a problem on long time scales and in an international context. Hedging, consumption smoothing over time, precautionary investments and liability are not to be presented under the heading of insurance, not only because this unnecessarily and confusingly expands the traditional definition of insurance, but also because this could create a false sense of security. The impact of climate change on the profitability of the commercial insurance sector is not likely to be severe, as the insurance companies are capable of shifting changed risks to the insured, provided that they are properly and timely informed on the consequences of climate change.