Polychlorinated dibenzo-p-dioxins (PCDD), dibenzofurans (PCDF), and biphenyls (PCB) are industrial compounds or by-products that have been widely identified as environmental contaminants, and residues have been detected in fish, wildlife, and humans. 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD; dioxin) is the most toxic member of this class of halogenated aromatic hydrocarbons (HAH); mechanistic studies indicate that the toxic and biochemical effects associated with exposure to TCDD are mediated via initial binding to the cytosolic aryl hydrocarbon (Ah) receptor protein present in target tissues and organs. Several other 2,3,7, 8-substituted PCDD and PCDF and non-ortho substituted PCB also bind to the Ah receptor and induce toxic responses similar to those for TCDD. Moreover, for these HAH there is a rank order correlation between their structure-Ah receptor binding and structure-toxicity relationships, and this supports a role for the Ah receptor in mediating these responses. Thus, the toxic equivalency factor (TEF) approach for HAH is based on the common mechanism of action for TCDD and related compounds in which a TEF value for a "dioxin-like" congener is defined as the potency of the individual (i) congener relative to TCDD ([EC50 [TCDD]/EC50 [test compound]). The toxic or dioxin equivalent (TEQ) for a mixture of HAH is defined by the following equation: TEQ = sigma [PCDDi] x TEFi + sigma [PCDFi] x TEFi. Industrial emissions and environmental and food residues contain complex mixtures of HAH (exodioxins) and the TEF/TEQ approach is used to regulate emissions and estimate the potential exposure and possible adverse health effects of exodioxins. The TEF approach for risk assessment of exodioxins makes a number of assumptions, including response additivity for individual compounds in a mixture of HAH. This review documents some of the following problems and limitations of the TEF approach: 1) environmental and food residues of HAH contain "non-dioxin-like" PCB that exhibit "antidioxin" activity for some responses; 2) the human diet contains endogenous Ah receptor ligands (endodioxins) such as polynuclear aromatic hydrocarbons (PAH), aromatic amines in cooked foods, indole-3-carbinol (I3C), and related hetero-PAH in cruciferous vegetables. Mass balance and mass potency estimates for human dietary intakes suggest that for some responses the effects of natural or endodioxins may be greater than those of exodioxins; and 3) I3C, a weak Ah receptor agonist, also exhibits Ah receptor antagonist activity, and interactions between I3C and endodioxins may inhibit or inactivate some toxic responses and decrease TEQ(Exodioxin).