The paper reviews the state-of-the-art in computational modeling of thrombus formation and growth and related phenomena including platelet margination, activation, adhesion, and embolization. Presently, there is a high degree of empiricism in the modeling of thrombus formation. Based on the experimentally observed physics, the review gives useful strategies for predicting thrombus formation and growth. These include determining blood components involved in atherosclerosis, effective blood viscosity, tissue properties, and methods proposed for boundary conditions. In addition to the guidelines, ongoing research on the effect of shear stress on platelet margination, activation and adhesion, and platelet-surface interactions are reviewed. Biotechnol. Bioeng. 2017;114: 2154-2172. (c) 2017 Wiley Periodicals, Inc.