New materials can potentially reduce the cost and improve the efficiency of solar photovoltaics, batteries, and catalysts, leading to broad societal impact. This talk describes a computational approach to materials design in which density functional theory (DFT) calculations are performed over very large computing resources. Because DFT calculations accurately predict many properties of new materials, this approach can screen tens of thousands of potential materials in short time frames. We present some major software development efforts that generated over 8 million CPU-hours worth of materials information in the span of a few months, identifying several new Li ion battery cathode materials that were verified experimentally. This represents one of the largest materials data sets ever computed, and the results are compiled on a public web site (The Materials Project) with over 3,000 registered users that are designing new materials with computed information. Finally, we describe future efforts in which algorithms might "self-learn" which chemical spaces are the most promising for investigation based on the results of previous computations, with application to solar water splitting materials.