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The difficulties encountered in extrapolating biological activity from cigarette smoke composition provide generally applicable lessons as they are representative of the problems encountered with other complex mixtures. Researchers attempting to assess risk are faced with attempting to interpret data from a number of areas including: tobacco science; smoke/aerosol chemistry specific to tobacco; sophisticated analytical chemistry applications and techniques for trapping, collecting, separating, and quantifying very specific compounds at nanogram to picogram levels; numerous biological testing methodologies; and animal models of tumors and carcinogenesis. Numerous hypotheses have been developed over the past five decades and tested with the technology of the day in attempts to interpret the biological activity of cigarette smoke in relation to the chemistry of this complex mixture. These hypotheses fall into several categories discussed in this review: mechanisms of pyrogenesis of polycyclic aromatic hydrocarbons (PAHs) in tobacco smoke; levels of PAHs in cigarette mainstream smoke (MS) and its tumorigenicity in mouse skin-painting experiments; control of PAH levels in MS; chemical indicators of cigarette smoke condensate (CSC) tumorigenicity; control of levels of MS components partitioned between the vapor phase and particulate phase of MS; tumorigenic threshold limits of CSC and many of its components; tumorigenic aza-arenes in tobacco smoke; MS components reported to be ciliastatic to smokers' respiratory tract cilia; anticarcinogenic tobacco-smoke components. Of 52 hypotheses reviewed in this paper, 15 have excellent data supporting the hypothesis based on today's technology. The remaining 37 hypotheses, although originally plausible, have since become insupportable in light of new and contradictory data generated over the years. Such data were generated sometimes by the original authors of the hypotheses and sometimes by other investigators. The hypotheses presented today are less likely to be supplanted because they are well conceived and have a strong mechanistic basis. The challenge for the future is the generation and interpretation of data relating the chemistry and biological activity associated with the dynamic and complex mixture of tobacco smoke.