Fluid-structure interaction problems appear in many areas. In the present lecture
we will concentrate on specific problems arising in hemodynamics. The aim will
be to study the resulting  nonlinear coupled system from analytical as well
as numerical point of view. We address theoretical questions of well-posedness and
present an efficient and robust numerical scheme in order to simulate blood flow in
compliant vessels. With respect to the numerical simulations we will in particular
discuss the questions of the added mass effect, stability and convergence order. We
will present results of numerical simulations and demonstrate the efficiency of new
kinematic splitting scheme.