A wide variety of artificial intelligence (AI) and structure-activity relationship (SAR) approaches have been applied to tackling the general problem of predicting rodent chemical carcinogenicity. Given the diversity of chemical structures and mechanisms relative to this endpoint, the shared challenge of these approaches is to accurately delineate classes of active chemicals representing distinct biological and chemical mechanism domains, and within those classes determine the structural features and properties responsible for modulating activity. In the following discussion, we present a survey of AI and SAR approaches that have been applied to the prediction of rodent carcinogenicity, and discuss these in general terms and in the context of the results of two organized prediction exercises (PTE-1 and PTE-2) sponsored by the US National Cancer Institute/National Toxicology Program. Most models participating in these exercises were successful in identifying major structural-alerting classes of active carcinogens, but failed in modeling the more subtle modifiers to activity within those classes. In addition, methods that incorporated mechanism-based reasoning or biological data along with structural information outperformed models limited to structural information exclusively. Finally, a few recent carcinogenicity-modeling efforts are presented illustrating progress in tackling some aspects of the carcinogenicity prediction problem. The first example, a QSAR model for predicting carcinogenic potency of aromatic amines, illustrates that success is possible within well-represented classes of carcinogens. From the second example, a newly developed FDA/OTR MultiCASE model for predicting the carcinogenicity of pharmaceuticals, we conclude that the definitions of biological activity and nature of chemicals in the training set are important determinants of the predictive success and specificity/sensitivity characteristics of a derived model.