We describe recent advances in the empirical analysis of insurance markets. This new research proposes ways to estimate individual demand for insurance and the relationship between prices and insurer costs in the presence of adverse and advantageous selection. We discuss how these models permit the measurement of welfare distortions arising from asymmetric information and the welfare consequences of potential government policy responses. We also discuss some challenges in modeling imperfect competition between insurers, and outline a series of open research questions. JEL classification numbers: C51, D82. Keywords: Insurance markets; Asymmetric information; Adverse selection.