Building processing, structure, and property (PSP) relations for computational materials design is at the heart of the Materials Genome Initiative in the era of high-throughput computational materials science. Recent technological advancements in data acquisition and storage, microstructure characterization and reconstruction (MCR), machine learning (ML), materials modeling and simulation, data processing, manufacturing, and experimentation have significantly advanced researchers' abilities in building PSP relations and inverse material design. In this article, we examine these advancements from the perspective of design research. In particular, we introduce a data-centric approach whose fundamental aspects fall into three categories: design representation, design evaluation, and design synthesis. Developments in each of these aspects are guided by and benefit from domain knowledge. Hence, for each aspect, we present a wide range of computational methods whose integration realizes data-centric materials discovery and design.