The arteries deliver blood from the heart to tissues, while the veins return blood to the heart. Although we sometimes think of arteries and veins as simple tubes, in reality they are much more complex: they curve and branch, which profoundly influences blood flow and biomechanical forces within the arterial wall. The artery wall is composed of several types of cells that interact with each other and can respond to biomechanical forces. Computational tools help us better understand the relationship between arterial geometric complexity, arterial biomechanics, and arterial wall biology.