We develop a quantitative theory of mortality trends and population dynamics. We emphasize diseases as causes of death and individuals' decisions to reduce their mortality by adopting, at some cost, a modern health-related technology. Adoption confers a dynamic externality: Adoption becomes cheaper as more individuals acquire the modern technology. Our model generates an S-shaped diffusion curve, whose shape dictates the pace of mortality reduction in each country. We use the model to explain the gradual decline of mortality in Western Europe in the 19th and 20th centuries as well as the rapid decline in poor countries since 1960. Unlike a Malthusian theory of population, our model accounts for the well-known historical disconnect between mortality decline and economic takeoff and its recent equivalents: cross-country mortality convergence despite lack of income convergence and mortality miracles, i.e., declining mortality in countries with declining income. Our model is also consistent with the observed acceleration in world population, which cannot be explained solely by declining fertility à la Becker.