Results of ongoing theoretical computational studies of blood flow in arteriolar and venular bifurcations are presented. In arteriolar bifurcations, the blood is modeled as a two-phase continuum, with a central core that is a concentrated suspension of red blood cells and with a layer of plasma adjacent to the vessel wall; the fluids are assumed to be Newtonian with different constant viscosities. The evolution of the two phases as the blood flows through the arteriolar bifurcation is studied. In venular bifurcations, two converging streams are modeled as Quemada-type thixotropic fluids with different hematocrits. The streams are followed through the bifurcation as they fold and form a strongly asymmetric velocity profile at the outlet cross section. These models yield predictions of the hematocrit and the velocity distribution downstream from arteriolar and venular bifurcations. The implications of these results for blood flow in microvascular networks are discussed.