Health shocks are an important source of risk. People in bad health work less, earn less, face higher medical expenses, die earlier, and accumulate much less wealth compared to those in good health. Importantly, the dynamics of health are much richer than those implied by a low-order Markov process. We first show that these dynamics can be parsimoniously captured by a combination of some lag-dependence and ex-ante heterogeneity, or health types. We then study the effects of health shocks in a structural life-cycle model with incomplete markets. Our estimated model reproduces the observed inequality in economic outcomes by health status, including the income-health and wealth-health gradients. Our model has several implications concerning the pecuniary and non-pecuniary effects of health shocks over the life-cycle. The (monetary) lifetime costs of bad health are very concentrated and highly unequally distributed across health types, with the largest component of these costs being the loss in labor earnings. The non-pecuniary effects of health are very important along two dimensions. First, individuals value good health mostly because it extends life expectancy. Second, health uncertainty substantially increases lifetime inequality by affecting the variation in lifespans.