The blood vessels that run on the surface of the heart and through its muscle are compliant tubes that can be affected by the pressures external to them in at least two ways. If the pressure outside these vessels is higher than the pressure at their downstream ends, the vessels may collapse and become Starling resistors or vascular waterfalls. If this happens, the flow through these vessels depends on their resistance and the pressure drop from their inflow to the pressure around them and is independent of the actual downstream pressure. In the first part of this review, the physics of collapsible tubes is described, and the possible occurrences of vascular waterfalls in the body is evaluated. There is good evidence that waterfall behavior is seen in collateral coronary arteries and in extramural coronary veins, but the evidence that intramural coronary vessels act like vascular waterfalls is inconclusive. There is no doubt that in systole there are high tissue pressures around the intramyocardial vessels, particularly in the subendocardial muscle of the left ventricle. The exact nature and values of the forces that act at the surface of the small intramural vessels, however, are still not known. We are not certain whether radial (compressive) or circumferential and longitudinal (tensile) stresses are the major causes of vascular compression; the role of collagen struts in modifying the reaction of vessel walls to external pressures is unknown but possibly important; direct examination of small subepicardial vessels has failed to show vascular collapse. One of the arguments in favor of intramyocardial vascular waterfalls has been that during a long diastole the flow in the left coronary artery decreases and reaches zero when coronary arterial pressure is still high: it can be as much as 50 mmHg in the autoregulating left coronary arterial bed and approximately 15-20 mmHg even when the vessels have been maximally dilated. These high zero flow pressures, especially during maximal vasodilatation, have been regarded as indicating a high back pressure to flow that is due to waterfall behavior of vessels that are exposed to tissue pressures.(ABSTRACT TRUNCATED AT 400 WORDS)