People have very different beliefs about the risks they face. I analyse how heterogeneous risk perceptions affect the insurance contracts offered by profit-maximising firms. An essential distinction is how risk perceptions affect the willingness to pay for insurance relative to the willingness to exert risk-reducing effort. This determines both the sign of the correlation between risk and insurance coverage in equilibrium, shedding new light on a recent empirical puzzle, and the type of individuals screened by either monopolistic or competing firms. Even with perfect competition, heterogeneous risk perceptions may well strengthen the case for government intervention in insurance markets.