The main objective of this study is to highlight recent advances in the biomechanical analysis of the carotid artery. This artery plays a critical role in supplying blood to the brain and face but is vulnerable to atherosclerosis—an obstruction caused by the accumulation of lipid particles over time. Such blockages can lead to serious health risks, including stroke. Treatment typically involves medication or the insertion of stents to restore blood flow. While the mechanical properties of the carotid artery have historically received limited attention, recent studies have made significant progress using the finite element method (FEM). This computational method, often based on medical imaging such as CT or MRI, allows researchers to model and analyze the artery’s structural and hemodynamic behavior under pathological conditions. Numerical results obtained through FEM have shown strong agreement with clinical data, confirming their reliability in simulating disease scenarios. Additionally, research has demonstrated that altered blood flow due to vascular diseases can deform the artery’s geometry, further impeding circulation. Advances in modeling techniques have not only improved our understanding of carotid artery biomechanics but also contributed new tools for clinical evaluation and treatment planning.