A contemporary trend in computational toxicology is the prediction of toxicity endpoints and toxic modes of action of chemicals from parameters that can be calculated directly from their molecular structure. Topological, geometrical, substructural, and quantum chemical parameters fall into this category. We have been involved in the development of a new hierarchical quantitative structure-activity relationship (QSAR) approach in predicting physicochemical, biomedicinal and toxicological properties of various sets of chemicals. This approach uses incremsingly more complex molecular descriptors for model building in a graduated manner. In this paper we will apply statistical and neural net mettlods in the development of QSAR models for predicting toxicity of chemicals using topostructural, topochemical, geometrical, and quantum chemical indices. The utility and limitations of the approach will be discussed.