Extreme weather events and their associated monetary impacts are expected to rise globally due to climate change. The trend of rising costs of extreme weather events poses a number of challenges for the insurance sector. This chapter summarizes insurance supply arrangements that currently exist for natural disasters and possible reforms of the way in which insurance is supplied to cope with climate change. Moreover, empirical evidence of demand for insurance against climate risk is reviewed, with a focus on possible explanations for why this demand is often low in practice. Several implications of climate change for future natural disaster insurance demand are discussed as well. Strategies for how insurance arrangements, complemented with other policies, can stimulate climate change adaptation by policyholders are highlighted. Furthermore, the chapter summarizes the state-of-the-art catastrophe models for assessing climate risk for insurance design, including their advantages and pitfalls. Based on the outcomes of our investigation, key implications for insurers and policymakers are drawn, and an agenda for future research is outlined.