The landscape of workflow systems for scientific applications is notoriously convoluted with hundreds of seemingly equivalent workflow systems, many isolated research claims, and a steep learning curve. To address some of these challenges and lay the groundwork for transforming workflows research and development, the WorkflowsRI and ExaWorks projects partnered to bring the international workflows community together. This paper reports on discussions and findings from two virtual “Workflows Community Summits” (January and April, 2021). The overarching goals of these workshops were to develop a view of the state of the art, identify crucial research challenges in the workflows community, articulate a vision for potential community efforts, and discuss technical approaches for realizing this vision. To this end, participants identified six broad themes: FAIR computational workflows; AI workflows; exascale challenges; APIs, interoperability, reuse, and standards; training and education; and building a workflows community. We summarize discussions and recommendations for each of these themes.