This paper argues that the financial exposure of households and firms to natural catastrophe disasters is borne primarily by insurance companies. Surprisingly, insurers use reinsurance to cover only a small fraction of these exposures, yet many insurers do not have enough capital and surplus to survive medium or large disasters. In a well-functioning financial system, these risks would be more widely shared. This paper articulates eight different explanations that may lie behind the limited risk sharing, relating them both to recent industry developments and financial theory. I then examine how financial innovation can help change the equilibrium toward a more efficient outcome.