In response to a request from the National Oceanic and Atmospheric Administration - and with the support of the National Aeronautics and Space Administration and the National Science Foundation - the National Academies of Sciences, Engineering, and Medicine conducted a two-part virtual workshop, "Space Weather Operations and Research Infrastructure," on June 16-17 and September 9-11, 2020. The overall goals of the workshop were to review present space weather monitoring and forecasting capabilities, to consider future observational infrastructure and research needs, and to consider options toward the further development of an effective, resilient, and achievable national space weather program. This publication summarizes the presentation and discussion of the workshop.