International audienceArterial flow is a three-dimensional unsteady process that is analyzed by measurements as well as physiological, biological, and mechanical experiments and numerical simulations. Few quantities can be noninvasively measured; they encompass cardiac frequency and peripheral arterial blood pressure as well as velocity and flow rate in given arterial stations by functional imaging. The central arterial blood pressure, from which clinicians derive several indices that are related to the physiological state of compartments of the cardiovascular apparatus, is measured using catheter-based transducers. Research is carried out to adequately infer the aortic pressure from measures in peripheral arteries using efficient signal processing.Blood flows through deformable arteries that dilate and constrict. The expansion of elastic arteries (Windkessel effect) that constitute the upstream compartment of the arterial tree transforms the systolic bolus into a pulsatile flow. Furthermore, the perfusion of the cardiac pump by coronary arteries benefits from the backflow generated by the wall recoil in elastic arteries. However, the arterial deformation is not only passive but also active. Mural cells sense and react to the stress field and adjust the caliber of the arterial lumen accordingly using intra-, auto-, juxta-, and paracrine signaling. The arterial wall is innervated and perfused from the lumen and vasa vasorum, hence receiving nervous and endocrine cues that are transduced for appropriate outputs. The vasomotor tone determines the level of the flow resistance.The regulation of the arterial flow has been widely investigated by physiologists, exhibiting the intricated and complex mechanisms that control the body’s homeostasis and adapt the local blood supply to the needs. At lower length scales, biologists describe the entire set of regulators and demonstrate their respective role and the functioning of signaling pathways in normal and pathological conditions. Biomechanicians develop new methods to assess the rheology and behavior of living tissues and, in collaboration with applied mathematicians, model physiological and pathophysiological processes. Some mechanical aspects that are easily handled in mechanics (e.g., applied to civil engineering and aeronautics) cannot be directly used in biomechanics. First, the architecture and the structure are much more complicated. Second, blood is carried in arterial lumens surrounded by three-layered walls made of composite materials. Both blood and wall are biological tissues, water being a major component. Hence, the fluid–structure interaction problem requires specific numerical treatment and elaboration of proper algorithms and multiphysics coupling softwares. Numerical tests are nevertheless carried out using simplifying assumptions and can be useful in medical practice