In order to better understand the expanding and diverse requirements of the science and engineering community and the importance of a new broader range of advanced computing infrastructure, the NSF requested that the National Research Council carry out a study examining anticipated priorities and associated tradeoffs for advanced computing. Future Directions for NSF Advanced Computing Infrastructure to Support U.S. Science and Engineering in 2017-2020 provides a framework for future decision-making about NSF's advanced computing strategy and programs. It offers recommendations aimed at achieving four broad goals: (1) position the U.S. for continued leadership in science and engineering, (2) ensure that resources meet community needs, (3) aid the scientific community in keeping up with the revolution in computing, and (4) sustain the infrastructure for advanced computing.