The flow behavior of vesicles and cells is important in many applications in biology and medicine. For example, the flow properties of blood in micro-vessels is determined by the rheological properties of the red blood cells. Furthermore, microfluidic devices have been developed recently, which allow the manipulation of small amounts of suspensions of particles or cells. Another interesting biological system are sperm cell and cilia, which move actively in a fluid. Due to the large length- and time-scale gap between the atomic and the mesoscopic domain in soft matter systems, several mesoscale simulation techniques have been developed in recent years to study their hydrodynamic behavior. We have investigated one of these techniques, multi-particle-collision dynamics, in some detail. In particular, it has been shown that the method properly describes hydrodynamic interactions at low Reynolds numbers, if the parameters are in an appropriate range. This method has then be applied to study the dynamical bevavior of fluid vesicles and model red blood cells both in shear and capillary flows. Several types of dynamical behaviors as well as shape transformations occur as a function of shear rate (or flow ve- locity), membrane viscosity and internal viscosity. Sperm cell form clusters, and are hydrodynamically attracted to surfaces, and cilia arrays are synchronized by hydrody- namic interactions to form metachronal waves.