Ventricular assist devices (VADs) have revolutionized the care of end-stage heart failure, yet thromboembolic complications continue to challenge their utility in clinical use. At the heart of this challenge lies a paradox -- despite the incidence of thromboembolic stroke in VAD patients, explanted pumps are frequently found to be thrombus-free! This paradox suggests that the clots responsible for devastating neurological events like ischemic stroke, etc., form, detach, and embolize, leaving no trace behind. This process, called thrombus embolization, is a grossly underexplored problem. This is primarily due to the complex interplay of multiple physics that govern it, including the material heterogeneity of a clot, hemodynamic force-induced adhesive and cohesive fracture. To address this problem, sophisticated computational frameworks are developed in this thesis. First, a fast multiphase framework for blood flow is introduced that accounts for the multiconstituent nature of blood and has provisions to be coupled with thrombogenesis models to help predict thrombus composition. Next, peridynamics (PD) is adopted as the computational framework for modeling adhesive and cohesive fracture of blood clots. PD is particularly well-suited for this problem, as it naturally handles crack initiation, propagation, and fragmentation without special numerical treatment. PD is subsequently coupled with computational fluid dynamics (CFD) to enable the study of the full-scale problem in its complete complexity. This coupling is agnostic to the fluid mesh discretization. Furthermore, it is shown that the PD-CFD framework extends beyond its intended application and can be used to study the governing physics and optimize outcomes of clinical interventions such as thrombectomy and thrombolytic therapy. All results obtained using the proposed computational models were validated rigorously against experiments.