The fluid forces at the interface between the endothelium and flowing blood act as a link between the complex arterial hemodynamics and adverse biological events triggering vascular atherosclerosis onset and progression. Evidences of such a link have led to formulate the so-called hemodynamic risk hypothesis, suggesting a pivotal role of flow disturbances in vascular pathophysiology. In turn, the hemodynamic risk hypothesis has stimulated the development of a discipline, the computational hemodynamics, where medical imaging and computer simulations are integrated to quantitatively investigate the local hemodynamics in personalized cardiovascular models. Driven by in vitro experiments, wall shear stress (WSS), the frictional force per unit area exerted by the flowing blood on the endothelium, has been identified as a localizing factor of vascular dysfunction. However, the intravascular hemodynamic richness in large arteries distils into multifaceted WSS profiles, presenting marked multidirectionality as well as marked spatiotemporal variability along the cardiac cycle. The result is that the established paradigm based on WSS magnitude and directional changes along the cardiac cycle only partially accounts for the evolution of atherosclerotic lesions. In this scenario, the analysis of the WSS topological skeleton (TS), which is composed by fixed points and by expansion/contraction regions connecting them, has received growing interest because of its ability to identify e.g., flow separation, stagnation, and recirculation regions, which are known to be preferential sites for atherosclerotic lesions development. Methods for WSS TS characterization have been recently successfully proposed and applied to computational hemodynamics models with robust findings suggesting that WSS TS peculiar features: (i) are surrogate markers of near-wall transport of biochemicals; (ii) predict myocardial infarction in coronary arteries, early atherosclerosis changes in coronary arteries, and long-term restenosis after carotid endarterectomy. In this work, Lagrangian- and Eulerian-based methods for WSS TS characterization are presented and discussed together with recent findings from their application in a computational hemodynamics framework which confirm the potency of the WSS TS analysis as an effective biomechanical tool for elucidating the mechanistic link between flow disturbances and atherosclerosis