The objective of our session at the International Bio-Fluid Mechanics Symposium and Workshop was at the International Bio-Fluid Mechanics Symposium and Workshop to review the state-of-the-art in, and identify future directions for, imaging and computational modeling of blood flow in the large arteries and the microcirculation. Naturally, talks in other sessions of the workshop overlapped this broad topic, and so here we summarize progress within the last decade in terms of the technical development and application of flow imaging and computing, rather than the knowledge derived from specific studies. We then briefly discuss ways in these tools may be extended, and their application broadened, in the next decade. Furthermore, owing to the conceptual division between the hemodynamics of large arteries, and those within the microcirculation, we review these regimes separately: The former here by Steinman and Taylor; and the latter in a separate paper by Cristini.