The heart is the first organ to function in vertebrate embryos. The human heart, for example, starts beating around the 21st embryonic day. During the initial phase of its pumping action, the embryonic heart is seen as a pulsating blood vessel that is built up by (1) an inner endothelial tube lacking valves, (2) a middle layer of extracellular matrix, and (3) an outer myocardial tube. Despite the absence of valves, this tubular heart generates unidirectional blood flow. This fact poses the question how it works. Visual examination of the pulsating embryonic heart tube shows that its pumping action is characterized by traveling mechanical waves sweeping from its venous to its arterial end. These traveling waves were traditionally described as myocardial peristaltic waves. It has, therefore, been speculated that the tubular embryonic heart works as a technical peristaltic pump. Recent hemodynamic data from living embryos, however, have shown that the pumping function of the embryonic heart tube differs in several respects from that of a technical peristaltic pump. Some of these data suggest that embryonic heart tubes work as valveless "Liebau pumps." In the present study, a review is given on the evolution of the two above-mentioned theories of early cardiac pumping mechanics. We discuss pros and cons for both of these theories. We show that the tubular embryonic heart works neither as a technical peristaltic pump nor as a classic Liebau pump. The question regarding how the embryonic heart tube works still awaits an answer.