Recent advances in blood flow modeling have provided highly resolved, four-dimensional data of fluid mechanics in large vessels. The motivation for such modeling is often to better understand how flow conditions relate to health and disease, or to evaluate interventions that affect, or are affected by, blood flow mechanics. Vessel geometry and the pulsatile pumping of blood leads to complex flow, which is often difficult to characterize. This article discusses a computational method to better characterize blood flow kinematics. In particular, we compute Lagrangian coherent structures (LCS) to study flow in large vessels. We demonstrate that LCS can be used to characterize flow stagnation, flow separation, partitioning of fluid to downstream vasculature, and mechanisms governing stirring and mixing in vascular models. This perspective allows valuable understanding of flow features in large vessels beyond methods traditionally considered.