Future Directions for NSF Advanced Computing Infrastructure to Support U.S. Science and Engineering in 2017-2020 examines priorities and associated tradeoffs for advanced computing in support of NSF-sponsored science and engineering research. This report is an initial compilation of issues to be considered as future NSF strategy, budgets, and programs for advanced computing are developed. Included in the report are questions on which the authoring committee invites comment. We invite your feedback on this report, and more generally, your comments on the future of advanced computing at NSF.