This chapter presents an overview of recent works aimed at characterizing the mechanical behaviour of the human aorta via experiments, modeling and simulation. The application of these techniques are in particular detailed in the analysis of the following cases: ascending aorta, aortic arch and thoracic descending aorta under in-vitro and in-vivo conditions. The experimental procedure encompasses uniaxial tension and pressurization tests on healthy and pathological tissues of different ages. The tensile measurements are used to calibrate the material parameters of isotropic or anisotropic quasi-static elastic constitutive models which are intended to predict the material response in a wide deformation range. Although this task is usually carried out analytically, numerical simulations (using a discretized formulation defined in the context of the finite element method) are also performed for problems in which more complex geometry, boundary conditions and loads are considered. Overall, the reported material characterization was found to provide a realistic description of the mechanical behaviour of the aorta subjected to various deformation and stress scenarios. Finally, the implication of these studies is the possibility to predict the mechanical response of the human aorta under generalized loading states like those that can occur in physiological conditions and/or in medical device applications.