The quantitative assessment of toxicological data on the carcinogenic potential of chemicals requires consideration of a number of factors, including mathematical models of the mechanism of carcinogenic action and pharmacokinetic models for the metabolic activation of the parent compound to its reactive metabolite. In this article, the use of such models in estimating carcinogenic potency and in predicting risks at low levels of exposure is discussed, along with other factors involved in the evaluation of carcinogen bioassay data. The Carcinogenic Potency Database (CPDB) established by Gold et al. (1984, Environ. Health Perspect. 58, 9-322) is used to illustrate the application of quantitative approaches to carcinogenic risk assessment and to examine the variation in the potency of chemical carcinogens. Based on an analysis of 585 experiments selected from the CPDB, the risk-specific (10-6) doses (RSDs) obtained by linear extrapolation from the TD50 were generally within a factor of 5-10 of those derived from the linearized multistage model. The RSDs obtained by linear extrapolation from the TD50 are roughly lognormally distributed with a median of about 20-90 ng/kg/day, depending on the subset of the CPDB considered. This distribution has been used by Rulis (1986, in Food Protection Technology (C. W. Felix, Ed.), pp. 29-37, Lewis, Chelsea, MI) to explore the concept of a threshold of regulation for chemical carcinogens present in the environment at low levels. © 1990 Academic Press, Inc.