Human exposure to chemicals is rarely, if ever, limited to a single chemical. Therefore, it is essential that we consider multiple chemical effects and interactions in our risk assessment process. However, with the almost infinitely large number of chemical mixtures in the environment, systematic studies of the toxicology of these chemical mixtures with conventional methodologies and approaches are impossible because of the immense resources and unrealistically long durations required. Thus, the development of 'Predictive and Alternative Toxicology' is imperative. At Colorado State University (CSU), our research effort is entirely devoted to this challenge. In order to have a reasonable chance to deal with the complex issue of toxicology of chemical mixtures, we believe that the following concepts must be considered: (1) the utilization of computer, (2) the exploitation of mathematical/statistical methodologies; (3) developing very focused, mechanistically based, and short-term toxicology studies; (4) coupling computer/mathematical modeling with mechanistically-based toxicology. Our strategy therefore the utilization of physiologically-based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling, coupled with very focused, model-directed toxicology experiments as well as other statistical/mathematical methodologies such as Monte Carlo simulation, isobolographic analysis, and response surface methodology. We believe that 'Predictive and Alternative Toxicology' in terms of tissue dosimetry at the pharmacokinetic and pharmacodynamic levels is achievable with simple and complex but chemically defined mixtures. In this presentation, we describe two ongoing research projects as an illustration of our 'Bottom-Up' and 'Top-Down' approaches for handling the chemical mixtures: (1) PBPK/PD modeling of toxicologic interactions between Kepone and carbon tetrachloride (CCl4) and the coupling of Monte Carlo simulation for the prediction of acute toxicity; (2) the conceptual development of PBPK/PD modeling for a more complex chemical mixture of seven groundwater contaminants from hazardous waste sites and the consideration of subfractionation of this chemical mixture.