The mechanical integrity of arteries is of prime importance, for a proper oxygen and nutrients delivery to all organs. To optimize their mechanical properties, healthy arteries exhibit a complex hierarchical microstructure which ensures a sufficient compliance at low stresses and which stiffens at higher stresses, preventing over-dilatation. In this article, we propose a vast literature survey on how the mechanical properties of arteries are related to structural features. We first review the characteristics of arterial microstructure and composition and then we review the mechanical behavior of arteries. This allows evidencing, for the first time, the strong correlation existing between elastin and collagen contents within the arterial wall. However, bringing together most of the available mechanical tests on arterial walls shows the important variability of the mechanical arterial response. The presentation is organized at three different scales: at the tissue (macroscopic) scale, at the (micrometer) scale of the fiber networks, and at the (submicrometer) fibrillar and cellular scale. Glossary: Autoclave: pressure chamber used to carry out processes requiring elevated temperature and pressure different from ambient air pressure. In the sequel, autoclaving is used to separate soluble proteins (such as collagen) from non-soluble proteins (such as elastin). Constitutive relation: in mechanics, material-specific relation between stress and strain that characterizes the response of the material to an applied mechanical loading. In vivo pre stretch and pre stress: The in vivo state of the arterial tissue is not free of mechanical loading; in particular, it is subjected to an axial elongation and residual stresses. Staining: auxiliary technique used in microscopy to highlight structures in materials. For biological tissues, it involves the use of structure-specific dyes. Nomenclature: not needed