Combinatorial methods are high-efficiency methods to create large composition “libraries” of materials, for example, continuous composition variations, and test those compositions systematically in parallel for specific properties of interest, in contrast to the time-consuming one-composition-at-a-time approach. These methods have captured the attention of the materials industry with the promise of providing new discoveries “faster, better, and cheaper.” However, in the academic community, combinatorial methods often meet with less enthusiasm, perhaps due to the perception of combinatorial methodology as an Edisonian approach to science. The facts are quite to the contrary. In addition to impressive successes arising from the application of combinatorial methods to materials discovery, results coming out of systematic high-throughput investigations of complex materials phenomena (which would be too time-consuming or expensive to undertake) provide data leading to improvement in theories and models of materials chemistry and physics. Indeed, combinatorial methods provide a new paradigm for advancing a central scientific goal—the fundamental understanding of structure–property relationships of materials behavior.