Blood is a complex suspension of deformable particles, red blood cells, which exhibits a sophisticated dynamics when flowing in the microvasculature. Most of these complex phenomena, non-linear rheology, structuration of the suspension, heterogeneities of the hematocrit distribution, are directly connected to the rich microscopic dynamics of individual red blood cells, and their hydrodynamics interactions. We investigate a few aspects of the dynamics of red blood cells and giant vesicles - a simple model for RBCs. A study on the dynamics of very deflated vesicles, with shapes similar to those of red blood cells, shows that these objects which haven't received a lot of attention so far can exhibit richer than expected dynamics. We then mainly focus on the still unexplored problem of hydrodynamic interactions between vesicles or red blood cells and their consequences at the scale of the suspension. An experimental study of the interaction of two identical vesicles in shear flow shows that there is a net repulsion between the cells that leads to an increase of the distance between vesicles in a suspension. Scaling arguments are proposed for this interaction and a comparison with numerical results is performed and a quantitative estimation of a shear induced diffusion coefficient obtained by averaging the results for pair interactions is found. Finally, we investigate the diffusion of a cloud of red blood cells in Poiseuille flow in order to directly determine diffusion coefficients. The experiment shows that the cloud widens when traveling along the channel with a power law behaviour indicating sub-diffusion. This effect is confirmed by a theoretical analysis of a few limit cases.