Conventionally, the architecture of arteries is based around the close-packed smooth muscle cells and extracellular matrix. However, the adventitia and endothelium are now viewed as key players in vascular growth and repair. A new dynamic picture has emerged of blood vessels in a constant state of self-maintenance. Recent work raises fundamental questions about the cellular heterogeneity of arteries and the time course and triggering of normal and pathological remodelling. A common denominator emerging in hypertensive remodelling is an early increase in adventitial cell density suggesting that adventitial cells drive remodelling and may initiate subsequent changes such as re-arrangement of smooth muscle cells and extracellular matrix. The organization of vascular smooth muscle cells follows regular arrangements that can be modelled mathematically. In hypertension, new patterns can be quantified in these terms and give insights to how structure affects function. As with smooth muscle, little is known about the organization of the vascular endothelium, or its role in vascular remodelling. Current observations suggest that there may be a close relationship between the helical organization of smooth muscle cells and the underlying pattern of endothelial cells. The function of myoendothelial connections is a topic of great current interest and may relate to the structure of the internal elastic lamina through which the connections must pass. In hypertensive remodelling this must present an organizational challenge. The objective of this paper is to show how the functions of blood vessels depend on their architecture and a continuous interaction of different cell types and extracellular proteins.