The increasing demands of sustainable energy, electronics, and biomedical applications call for next-generation functional materials with unprecedented properties. Of particular interest are emerging materials that display exceptional physical properties, making them promising candidates in energy-efficient microelectronic devices. As the conventional Edisonian approach becomes significantly outpaced by growing societal needs, emerging computational modeling and machine learning (ML) methods are employed for the rational design of materials. However, the complex physical mechanisms, cost of first-principles calculations, and the dispersity and scarcity of data pose challenges to both physics-based and data-driven materials modeling. Moreover, the combinatorial composition-structure design space is high-dimensional and often disjoint, making design optimization nontrivial. In this Account, we review a team effort toward establishing a framework that integrates data-driven and physics-based methods to address these challenges and accelerate materials design. We begin by presenting our integrated materials design framework and its three components in a general context. We then provide an example of applying this materials design framework to metal-insulator transition (MIT) materials, a specific type of emerging materials with practical importance in next-generation memory technologies. We identify multiple new materials which may display this property and propose pathways for their synthesis. Finally, we identify some outstanding challenges in data-driven materials design, such as materials data quality issues and property-performance mismatch. We seek to raise awareness of these overlooked issues hindering materials design, thus stimulating efforts toward developing methods to mitigate the gaps.