It has long been recognized that the forces and stresses produced by the blood flow on the walls of the cardiovascular system are central to the development of different cardiovascular diseases (CVDs). However, up to now, the reason why arterial diseases occur at preferential sites is still not fully understood. This paper reviews the progress, made largely within the last decade, towards the use of 3D computational fluid dynamics (CFD) models to simulate the blood flow dynamics and its interaction with the arterial wall within the human thoracic aorta (TA). We describe the technical aspects of model building, review methods to create anatomic and physiologic models, obtain material properties, assign boundary conditions, solve the equations governing blood flow, and describe the assumptions used in running the simulations. Detailed comparative information is provided in tabular format about the model setup, simulation results, and a summary of the major insights and contributions of each TA article reviewed. Several syntheses are given that summarize the research carried out by influential research groups, review important findings, discuss the methods employed, limitations, and opportunities for further research. We hope that this review will stimulate computational research that will contribute to the continued improvement of cardiovascular health through a strong interaction and cooperation between engineers and clinicians. © 2013 Biomedical Engineering Society.