Most research on the effects of chemicals on biologic systems is conducted on one chemical at a time. However, in the real world people are exposed to mixtures, not single chemicals. Although various substances may have totally independent actions, in many cases two substances may act at the same site in ways that can be either additive or nonadditive. Many even more complex interactions may occur if two chemicals act at different but related targets. In the extreme case there may be synergistic effects, in which case the effects of two substances together are greater than the sum of either effect alone. In reality, most persons are exposed to many chemicals, not just one or two, and therefore the effects of a chemical mixture are extremely complex and may differ for each mixture depending on the chemical composition. This complexity is a major reason why mixtures have not been well studied. In this review we attempt to illustrate some of the principles and approaches that can be used to study effects of mixtures. By the nature of the state of the science, this discussion is more a presentation of what we do not know than of what we do know about mixtures. We approach the study of mixtures at three levels, using specific examples. First, we discuss several human diseases in relation to a variety of environmental agents believed to influence the development and progression of the disease. We present results of selected cellular and animal studies in which simple mixtures have been investigated. Finally, we discuss some of the effects of mixtures at a molecular level.