Arterial bifurcation flow has been of special interest for some years because of its important role in the formation of atherosclerotic plaques and thrombi. To investigate the flow phenomena analytically, four major factors need to be accommodated--the three-dimensionality of a general bifurcation, the pulsatile nature of the laminar flow, the distensibility of the arterial wall and the non-Newtonian character of the blood. In this review, both engineering and medical aspects of each factor are carefully surveyed. It is demonstrated that the latest generation of computational fluid dynamics codes can treat this problem area and that it is both feasible and desirable to investigate the effects of each independent factor.