During the past ten years there has been development of relationships to predict physical, chemical, environmental, and toxicological properties of chemicals directly from structure. The fundamental framework of the approach is to propose a theoretical basis for such relationships, compile data to test these relationships, and modify the relationships on the basis of these tests. The essential elements of this process are (1) the development of mathematical descriptors that quantify different aspects of molecular structure; and (2) the use of multivariate statistical techniques to identify intrinsic dimensions of chemical structure and to develop structure-activity relationships (SAR) to predict the property of interest from structure. These relationships may be applied to any chemical data base because such relationships are derived from parameters which are nonempirical and algorithmically defined.