The stiffness and structural integrity of the arterial wall depends primarily on the organization of the extracellular matrix and the cells that fashion and maintain this matrix. Fundamental to the latter is a delicate balance in the continuous production and removal of structural constituents and the mechanical state in which such turnover occurs. Perturbations in this balance due to genetic mutations, altered hemodynamics, or pathological processes result in diverse vascular phenotypes, many of which have yet to be well characterized biomechanically. In this paper, we emphasize the particular need to understand regional variations in the biaxial biomechanical properties of central arteries in health and disease and, in addition, the need for standardization in the associated biaxial testing and quantification. As an example of possible experimental methods, we summarize testing protocols that have evolved in our laboratory over the past 8 years. Moreover, we note advantages of a four fiber family stress-stretch relation for quantifying passive biaxial behaviors, the use of stored energy as a convenient scalar metric of the associated material stiffness, and the utility of appropriate linearizations of the nonlinear, anisotropic relations both for purposes of comparison across laboratories and to inform computational fluid-solid-interaction models. We conclude that, notwithstanding prior advances, there remain many opportunities to advance our understanding of arterial mechanics and mechanobiology, particularly via the diverse genetic, pharmacological, and surgical models that are, or soon will be, available in the mouse.