In this paper, we present a survey of the two main problems of information in insurance markets: moral hazard and adverse selection. Both arise because the insurers are less informed than the insureds. Moral hazard is explained by the fact that the insurer cannot observe, ex ante, the activities of the insured who may have the incentive to change the state of the world in response to insurance coverage. Adverse selection arises since the insurer cannot determine without costs, the risks inherent in the individuals. After defining formally these two problems, we shall present different insurance strategies (private and public) with a view to correct them. In conclusion we shall propose some avenues of research.