Summarizing relative risk estimates across strata of a covariate is commonly done in comparative epidemiologic studies of incidence or mortality. Conventional Mantel-Haenszel and rate standardization techniques used for this purpose are strictly suitable only when there is no interaction between relative risk and the covariate, and tests for interaction typically are limited to examination for departures from linearity. Poisson regression modeling offers an alternative technique which can be used for summarizing relative risk and for evaluating complex interactions with covariates. A more general application of Poisson regression is its utility in modeling disease rates according to postulated etiologic mechanisms of exposures or according to disease expression characteristics in the population. The applications of Poisson regression analysis to problems of summarizing relative risk and disease rate modeling are illustrated with examples of cancer incidence and mortality data, including an example of a nonlinear model predicted by the multistage theory of carcinogenesis.