Heart valve, and subsequently cardiac function, may be seriously compromised as a result of stenosis or regurgitation. If necessary, the native heart valve is surgically replaced with an artificial substitute, which is in about 40% of the cases a bileaflet mechanical heart valve (BMHV). While generally showing excellent hemodynamic performance in the short term, current BMHVs are not free of clinical complications, which are induced by thrombus formation and hemolysis. Computational fluid dynamic (CFD) modeling is now considered a powerful and extremely useful tool to investigate blood flow in existing BMHVs and to reduce the costs associated with the development of new prototypes. A prerequisite for performing realistic heart valve simulations is the implementation of a fluid-structure interaction (FSI) algorithm that accounts for the mechanical interaction between the valve leaflets and the ambient blood. Provided the numerical resolution is sufficiently high, three-dimensional CFD-FSI models are able to compute the complex flow structures that exist in the vicinity of a BMHV. In order to get information about the valve's potential for platelet activation and blood hemolysis, these CFD models must be accompanied by appropriate mathematical models that describe the relation between fluid dynamic variables and the damage to blood corpuscles. This chapter provides an overview on the state of the art in computational flow simulations in BMHV and discusses various approaches taken to integrate blood damage accumulation models into flow simulations.