In the cardiovascular system, morphology and functionality are closely related. Altered flow conditions play an important role in the development of arterial disease. In turn, these flow conditions are modified by arterial wall changes. A detailed understanding of the local hemodynamic environment, the influence of wall modifications on flow patterns and the long-term adaptations of the vascular wall after surgical procedures can have useful clinical applications, especially in view of reconstruction and revascularization operations. Some of these alterations are not well-understood, making it quite difficult to foresee short- and long-term evolution of the atherosclerotic disease and to plan an aggressive approach. Computational fluid dynamics (CFD) allows the carrying out of simulations at low cost and in completely controlled conditions. Three different issues are relevant to this subject and are addressed in this paper: (1) the definition of suitable mathematical models; (2) pre-processing of clinical data; and (3) the development of appropriate numerical techniques