Abstract: As we know, the regular arterial flow is in the laminarflow regime. The blood flow properties, particularly, the shear stressesalong the blood vessel, and the sites where atherosclerosis develops, haveattracted tremendous researches in recent decades. It has been well knownthat the oscillating and low shear stresses play an important role in thedevelopment of vascular lesions. Unsteady irregularstress distributions are likely to prevail at the curved and bifurcatedvessels with side branches, where, due to complicated geometries,blood flows always contain flow separation or secondary motions difficult to be simulated and understood in fluid mechanics. In thispaper, the past studies on the transient multi-dimensionalblood flows in arterial stenosis or in arterial geometries relevant in theconditions of atherosclerosis are reviewed. We also make suggestionsfor the future possible studies of circulatory vascular flows and wish toprovide some food for though for further designs of bio-medicaldevices.