The use of mathematical modeling and numerical simulation to study blood circulation and related pathologies is an active interdiciplinary field of research. It has a great social and economical impact mainly due to cardiovascular diseases, that represent one of the leading causes of death and morbidity in industrialized countries. Due to the complexity of the human cardiovascular system, the use of computational models to study blood flow in healthy and pathological situations is a challenge to mathematicians and engineers. Nevertheless, it constitutes nowadays a reliable tool which is increasingly used in clinical applications, such as the placement of stents in arteries with atherosclerotic plaques, or the understanding of aneuerysm growth and rupture. In this article some of the fundamental aspects of mathematical modeling and numerical simulation of blood circulation will be described, highlighting in particular the pathological case of cerebral aneurysms.