Implantable blood recirculating devices have provided life saving solutions to patients with severe cardiovascular diseases. However, common problems of hemolysis and thromboembolism remain an impediment to these devices. In this article, we present a brief review of the work by several groups in the field that has led to the development of new methodologies that may facilitate achieving the daunting goal of optimizing the thrombogenic performance of blood recirculating devices. The aim is to describe work which pertains to the interaction between flow-induced stresses and the blood constituents, and that supports the hypothesis that thromboembolism in prosthetic blood recirculating devices is initiated and maintained primarily by the non-physiological flow patterns and stresses that activate and enhance the aggregation of blood platelets, increasing the risk of thromboembolism and cardioembolic stroke. Such work includes state-of-the-art numerical and experimental tools used to elucidate flow-induced mechanisms leading to thromboembolism in prosthetic devices. Following the review, the paper describes several efforts conducted by some of the groups active in the field, and points to several directions that should be pursued in the future in order to achieve the goal for blood recirculating prosthetic devices becoming more effective as destination therapy in the future.