Insight into the mechanical properties of the arterial wall can give valuable information concerning the understanding of pulse wave propagation in the arterial tree, the genesis and progress of atherosclerosis, vessel wall adaptation and remodelling, and the prediction of the effects of medical intervention, such as blood-pressure regulating drug admission, balloon angioplasty, and bypass surgery. A widely used approach to characterize the mechanical properties of arteries is based on a mixed experimental–numerical method, in which parameters of mathematical constitutive models are fitted to experimental stress–strain data. For wall remodelling studies (Machchyn et al., 2010) these parameters preferably are based on micro-structural information such as collagen content and morphology (Rezakaniha et al., 2011). A generic set of parameters can be obtained from ex-vivo experiments where stress-strain relations can be obtained for transmural pressures ranging from a non-physiological unloaded to physiological fully loaded configuration (van den Broek et al., 2011). If only clinical data at physiological loading are available, extra constraints on the parameter set can be used to obtain a unique characterization (van der Horst et al., 2011). Several aspects regarding the above mentioned micro-structural based models will be discussed during the presentation. For predictive models of pulse wave propagation, micro-structural based constitutive models must be casted into pressure-area relations, whereas, for prediction of adaptation and arterial wall remodeling, the dynamics of smooth muscle cell behavior must be taken into account. Both facets will be shed light upon and illustrated by results recently obtained.