Complex physics and biochemistry, the wide range of temporal and spatial scales to be captured, and the significant inter- and intraindividual variations make the description of the blood flow in the human aorta a difficult task. Although computational tools are mature, said aspects challenge aortic biomechanical models, and the approach must always be tailored to the question at hand. Besides being highly pulsatile, the curvature and tortuosity of the aortic geometry strongly impacts the flow dynamics with aortic pathologies may even lead to turbulent flow. In the following chapter, the characteristics of blood and different modeling approaches for rheology, species transport and thrombus/stenosis development will be addressed.