The subject of structure-activity relationships is central to the understanding of chemical/life interactions: in particular, the science of quantitative structure-activity relationships (QSAR) is the tool of choice for the rationalisation of these phenomena. As in classical QSAR applications to medicinal chemistry, various studies relative to individual classes of mutagens and carcinogens have shown how the potency of the active chemicals in each class varies according to variation of chemical structure/properties. However, in mutagenicity and carcinogenicity QSAR studies, the need for investigating the difference between active and non-active chemicals is of primary importance, since risk assessment is concerned with this issue, and with the potency of the active compounds. Moreover, the needs related to the practice of risk assessment have motivated attempts to construct general QSAR models (for example, for predicting chemical carcinogenicity), which are not tailored to congeneric series of chemicals, with the ambitious hope that these models would be valid for all kind of chemicals. Recent comparative exercises for the prediction of chemical carcinogens, held under the aegis of the US National Toxicology Program, have shown that several prediction systems were concordant in the identification of the powerful carcinogens, whereas many non-carcinogens were predicted to be positive by different systems. Thus, the clear limitation of almost all the prediction systems was their excessive sensitivity. This is because the various QSAR approaches essentially acted as gross "class-identifiers": they pointed to the presence or absence of alerting chemical functionalities, but were not able to make gradations within each potentially harmful class. The positive side of this overall picture is that, at this stage, we are capable of identifying most of the possible structural alerts (SA). This type of knowledge can already be used in setting priorities for experimentation, and in designing safer chemicals by avoiding those with the SAs. The big challenge of the present research is to acquire the ability to distinguish between potential and actual activity of the chemicals presenting the SAs.