The design and synthesis of materials with useful, novel properties is one of the most active areas of contemporary science, generating a veritable explosion of scientific activity in areas such as biomaterials, cell and tissue engineering, organic photovoltaics and light-emitting materials, and nanomaterials for a myriad of medical and nonmedical applications. This new era of materials design and discovery covers many disciplines from chemistry and biology to physics and engineering. The vast majority of this research effort is in experimental science, with theoretical and computational science lagging somewhat behind. Obviously, the ability to predict the properties of novel materials prior to synthesis, and to understand the relationships between the microscopic properties of molecular components and the macroscopic materials properties, would be of substantial benefit to materials designers. In view of the complexity of many new materials, there is a strong need for machine learning methods that can generate robust, predictive models linking these microscopic and macroscopic properties. The application of such methods to model materials properties is described as quantitative structureĀproperty relationship (QSPR) modeling. Although these, and closely related methods such as quantitative structureĀ activity relationships (QSAR), have proven to be very successful in other areas of molecular design, there is surprisingly little published work on their applications to materials, as can be seen in Figure 1. This review summarizes the most commonly used predictive, structureĀproperty modeling methods and their recent applications to materials design. There are no published reviews of this type of materials modeling, in spite of the small but increasing number of materials QSPR modeling papers appearing in the literature across a wide range of materials classes—nanomaterials, catalysts, biomaterials, polymers, ionic liquids, supercritical CO2, and ceramics, as shown in Figure 2. We anticipate that this comprehensive, critical review will be useful to a broad spectrum