In 1628, William Harvey provided definitive evidence that blood circulates. The notion that blood travels around the body in a circle raised the important question of how nutrients pass between blood and underlying tissue. Perhaps, Harvey posited, arterial blood pours into the flesh as into a sponge, only then to find its way into the veins. Far from solving this problem, Marcello Malpighi’s discovery of the capillaries in 1661 only added to the dilemma; surely, some argued, these entities are little more than channels drilled into tissues around them. As we discuss in this review, it would take over 200 years to arrive at a consensus on the basic structure and function of the capillary wall. A consideration of the history of this period provides interesting insights not only into the central importance of the capillary as a focus of investigation, but also the enormous challenges associated with studying these elusive structures.