We review the methodology used in the analysis of time-series studies of ambient air pollution. Our focus is on mortality studies, in which daily counts of death are correlated with changes in air pollution. We first illustrate the methods by showing data from the 1950s, during which the effects of air pollution were much more pronounced, and then describe current methods that were developed to identify associations when the signal-to-noise ratio is much lower. We describe basic data sources, details of statistical methods, and current state of the art, especially as it refers to problems found recently with the fitting algorithm used in the generalized additive models. A summary of the findings from mortality studies is presented and the pre-eminent issues regarding methods, interpretation, and identification of susceptible populations are discussed. We conclude by describing possible biological mechanisms and suggesting other designs that will aid in the interpretation of data from studies of acute health effects.