The review is an introduction to methods for evaluating structure-activity relationships (SARs), and, in particular, to those methods that have been applied to study mutagenicity and carcinogenicity. A brief history and some background material on the earliest attempts to correlate molecular structure and biological activity are included. Most of the discussion focuses on modern methods utilizing extrathermodynamic and physical property variables such as the Hansch method and SIMCA, and approaches based on molecular connectivity such as the ADAPT. CASE. and Enslein methods. In general, the latter class is potentially the most useful in the study of the large and structurally diverse databases so often encountered in the study of mutagenicity and carcinogenicity. They also are not very sensitive to lab-to-lab variances in reported activities and outright misclassifications in activities of some compounds. This is chiefly because the statistical treatments used in these methods tend to dilute the importance of outliers.