A review with 234 refs. Biol. properties of chem. compds. depend in a very sensitive way on their chem. structure. The understanding of such dependencies in terms of so-called structure-activity relationships is one of the principal goals of medicinal chem. and at the heart of modern computer-aided drug design (CADD). CADD methods have become an indispensable tool in the search for new drugs and may not only aid to guide exptl. work effectively but also to elucidate mechanisms of action at the mol. level. Because of the complexity of biol. matter and the huge no. of chem. structures and possible variations, a large no. of quite different CADD methods serving different purposes have been developed. These methods can be roughly categorized into (i) statistical approaches relating physicochem. parameters to biol. potency, (ii) heuristic methods usually based on substructural consideration, and (iii) mol. modeling with powerful interactive computer graphics as key instrument. Although the recent development has very much stressed mol. modeling the other methods are still very useful in many cases. This presentation will conc. on the first category, where so-called quant. structure-activity relationships (QSARs) are derived with biol. potency as dependent and physicochem. parameters as independent. These characterize hydrophobic, electronic and steric properties of drugs and are usually applied to characterize variations of substituents. The most important parameters and their phys. meaning will be discussed, together with specific aspects of their application to biol. problems. With typical examples from Hansch anal. important aspects of QSARs such as interpretability, predictive power, general QSARs know-how and limitations of QSARs approaches will be outlined. Alternative statistical methods such as classification methods or principal component anal. will also be briefly introduced.