Two strategies particularly useful for approaching the toxicology of complex mixtures are: (1) bioassay-directed chemical characterization; and, (2) comparative bioassay studies. Bioassay-directed fractionation and chemical characterization is a strategy for identifying biologically active compounds or compound classes in complex mixtures. The identification and assessment of mutagens and carcinogens in complex mixtures has been significantly advanced by the use of short-term genetic bioassays. Bioassay-directed fractionation coupled with new organic characterization methods has provided the tools needed to more efficiently identify potential carcinogens in complex mixtures. A comparative potency strategy for evaluating the relative toxicity, mutagenicity and carcinogenicity of a series of different mixtures has been used to provide comparative potency data for risk assessment. The comparative mutagenicity and carcinogenicity of a series of combustion emissions has been assessed using dose-response studies in bacteria, mammalian cells and rodents.