The historical development of the mechanics of blood flow can be traced from ancient times, to Leonardo da Vinci and Leonhard Euler and up to the present times with increasing biological knowledge and mathematical analysis. In the last two decades, quantitative and numerical methods have steadily given more complete and precise understanding. In the arterial system wave propagation computations based on nonlinear one-dimensional modeling have given the best representation of pulse wave propagation. In the veins, the theory of unsteady flow in collapsible tubes has recently been extensively developed. In the last decade, progress has been made in describing the blood flow at junctions, through stenoses, in bends and in capillary blood vessels. The rheological behavior of individual red blood cells has been explored. A working model consists of an elastic membrane filled with viscous fluid. This model forms a basis for understanding the viscous and viscoelastic behavior of blood.