Complex mixtures of polMyclic organic matter (POM) are used to illustrate the scientific problems and issues associated with characterizing the comparative risk ofrelated complex nmxtures. Thecomplexity of mixtures in whichthe active components are not well characterized present special challenges, which include identifying the critical components of mixtures, their sources, and the appropriate biomarker(s) ofexposure and dose; developing the appropriate experimental models for dose-response assessment; species extrapolation; and developing a scientific basis for pedkicting from one mixture to another. Strategies for addressing these issues include bioassay-direced chemical characterization of bioactive components of complex mixtures, apportionment methods to determine the source of biological activity and risk, DNA adduct methods to determine tissue exposure and target dose of mixtures, and comparative approaches to determining the relative similarity, potency, and risk of complex mixtures. Epidemiological data are available for humans exposed to POM from coke ovens, coal roofing tar, coal smoke, aluminum smelters, and cigarette smoke. These emissions are characterized and compared to POM from automotive emissions (diesel and gasoline), woodstove emnissions, residential oil furnace emissions, and ambient air particles. The tumor potency and estimated cancer risks for these POM mixtures ranges over nearly three orders of magnitude.