The quantitative structure-activity relationships method was popularized by Hansch and Fujita over 50 years ago. The usefulness of the method for drug design and development has been shown in the intervening years. As it was developed initially to elucidate which molecular properties modulated the relative potency of putative agrochemicals, and at a time when computing resources were scarce, there is much scope for applying modern mathematical methods to improve the QSAR method and to extending the general concept to the discovery and optimization of bioactive molecules and materials more broadly. I describe research over the past two decades where we have rebuilt the unit operations of the QSAR method using improved mathematical techniques, and have applied this valuable platform technology to new important areas of research and industry such as nanoscience, omics technologies, advanced materials, and regenerative medicine. This paper was presented as the 2017 ACS Herman Skolnik lecture.