Despite the many successes of arterial tissue engineering, clinically viable implants may be a decade or more away. Fortunately, there is much more that we can learn from native vessels with regard to designing for optimal structure, function, and properties. Herein, we examine recent observations in vascular biology from the perspective of nonlinear mechanics. Moreover, we use a constrained mixture model to study potential contributions of individual wall constituents. In both cases, the unique biological and mechanical roles of elastin come to the forefront, especially its role in generating and modulating residual stress within the wall, which appears to be key to multiple growth and remodeling responses.