The Mediterranean Sea provides a major route for heat and freshwater loss from the North Atlantic and thus is an important cause of the high density of Atlantic waters. In addition to the traditional view that loss of fresh water via the Mediterranean enhances the general salinity of the North Atlantic, and the interior of the eastern North Atlantic in particular, it should be noted that Mediterranean water outflowing at Gibraltar is in fact cooler than compensating inflowing water. The consequence is that the Mediterranean is also a region of heat loss from the Atlantic and contributes to its large-scale cooling. Uniquely, this system can be understood physically via the constraints placed on it by a single hydraulic structure: the Gibraltar exchange. Here we review the existing knowledge about the physical structure of the Gibraltar exchange today and the evidential basis for arguments that it has been different in the past. Using a series of quantitative experiments, we then test prevailing concepts regarding the potential causes of these past changes. We find that (1) changes in the vertical position of the plume of Mediterranean water in the Atlantic are controlled by the vertical density structure of the Atlantic; (2) a prominent Early Holocene "contourite gap" within the Gulf of Cadiz is a response to reduced buoyancy loss in the eastern Mediterranean during the time of "sapropel 1" deposition; (3) changes in buoyancy loss from the Mediterranean during MIS3 caused changes in the bottom velocity field in the Gulf of Cadiz, but we note that the likely cause is reduced freshwater loss and not enhanced heat loss; and (4) strong exchange at Gibraltar during Atlantic freshening phases implies that the Gibraltar exchange provides a strong negative feedback to reduced Atlantic meridional overturning. Given the very counterintuitive way in which the Strait of Gibraltar system behaves, we recommend that without quantitative supporting work, qualitative interpretations of how the system has responded to past external forcing are unlikely to be robust.