Microelectronics is a complex field with ever-evolving technologies and business needs, fueled by decades of continued fundamental materials science and engineering advancement. Decades of dimensional scaling have led to the point where even the name microelectronics inadequately describes the field, as most modern devices operate on the nanometer scale. As we reach physical limits and seek more efficient ways for computing, research in new materials may offer alternative design approaches that involve much more than electron transport e.g. photonics, spintronics, topological materials, and a variety of exotic quasi-particles. New engineering processes and capabilities offer the means to take advantage of new materials designs e.g. 3D integration, atomic scale fabrication processes and metrologies, digital twins for semiconductor processes and microarchitectures. The wide range of potential technological approaches provides both opportunities and challenges. The Materials, Processes, and R and D Challenges in Microelectronics Future Directions workshop was held June 23-24, 2022, at the Basic Research Innovation Collaboration Center in Arlington, VA, to examine these opportunities and challenges. Sponsored by the Basic Research Directorate of the Office of the Under Secretary of Defense for Research and Engineering, it is intended as a resource for the S and T community including the broader federal funding community, federal laboratories, domestic industrial base, and academia.