This article presents an overview of diverse material models used to represent the mechanical behavior of arteries and of the inverse problems posed by the identification of their constitutive parameters. After a brief introduction about the definition of inverse problems and about the general features of arteries, the article addresses three main questions involving inverse problems and arterial wall characterization: (1) macroscopic identification of the parameters of sophisticated constitutive models from traditional uniaxial and biaxial experiments; (2) mesoscopic identification of regional variations in the material parameters of arteries, tracking the effects of functional adaptation or lesions; (3) how constitutive models and inverse problems allow to obtain information on the arterial microstructure and how the structural constituents interact in the mechanical response. Finally, the article shows that a significant effort has been made so far to relate the complex mechanical behavior of arteries to their microstructure but a new class of inverse problems has recently appeared. It is related to the identification of mechanobiological parameters which are the parameters involved in the numerical models of growth and remodeling.