In the life sciences, including hemostasis and thrombosis, methods of structural biology have become indispensable tools for shedding light on underlying mechanisms that govern complex biological processes. Advancements of the relatively young field of computational biology have matured to a point where it is increasingly recognized as trustworthy and useful, in part due to their high space-time resolution that is unparalleled by most experimental techniques to date. In concert with biochemical and biophysical approaches, computational studies have therefore proven time and again in recent years to be key assets in building or suggesting structural models for membrane-bound forms of coagulation factors and their supramolecular complexes on membrane surfaces where they are activated. Such endeavors and the proposed models arising from them are of fundamental importance in describing and understanding the molecular basis of hemostasis under both health and disease conditions. We summarize the body of work done in this important area of research to drive forward both experimental and computational studies toward new discoveries and potential future therapeutic strategies.