Attempts have been made to formulate quantitative structure=activity relationships (QSARs) for the prediction of property/ bioactivity of chemicals from their experimental test data as well as properties that can be computed directly from molecular structure without the input of any other experimental property. Because both in drug design and hazard assessment of chemical scenarios relevant experimental data for property/ bioactivity estimation are not available for the majority of candidate chemicals, QSARs based on computed molecular descriptors are emerging as methods of choice for property/ bioactivity estimation in many cases. Numerical graph invariants or topological indices, viz., topostructural (TS) indices, topochemical (TC) indices, as well as three-dimensional (3-D) descriptors, and quantum chemical (QC) indices have been used for QSAR formulation based on computed descriptors. In the 1990s, Basak et al formulated the concept of hierarchical quantitative structure=activity relationships (HiQSAR) in which TS, TC, 3-D, and QC descriptors were used in a graduated manner, the more computationally demanding descriptors being used only if the simpler ones did not give acceptable QSAR models. Our experience with a substantial number of HiQSARs for physical, pharmacological, and toxicological properties of different congeneric as well diverse sets chemicals indicate that the combinations of TS + TC descriptors are capable of giving good quality QSARs in most situations. The addition of 3-D or QC descriptors make marginal or no improvement in model quality after the use of TS+ TC descriptors. At this age of “big data screening and analysis” this is a good news because QSARs derived from the less expensive and practically useful TS+ TC combination can be effective tools in the screening of large chemical libraries.