The Materials Genome Initiative (MGI) advanced a new paradigm for materials discovery and design, namely that the pace of new materials deployment could be accelerated through complementary efforts in theory, computation, and experiment. Along with numerous successes, new challenges are inviting researchers to refocus the efforts and approaches that were originally inspired by the MGI. In May 2017, the National Science Foundation sponsored the workshop “Advancing and Accelerating Materials Innovation Through the Synergistic Interaction among Computation, Experiment, and Theory: Opening New Frontiers” to review accomplishments that emerged from investments in science and infrastructure under the MGI, identify scientific opportunities in this new environment, examine how to effectively utilize new materials innovation infrastructure, and discuss challenges in achieving accelerated materials research through the seamless integration of experiment, computation, and theory. This article summarizes key findings from the workshop and provides perspectives that aim to guide the direction of future materials research and its translation into societal impacts.