There is lack of consensus concerning the three-dimensional arrangement of the myocytes within the ventricular muscle masses. Bioengineers are seeking to model the structure of the heart. Although the success of such models depends on the accuracy of the anatomic evidence, most of them have been based on concepts that are far from anatomical reality, which ignore many significant previous accounts of anatomy presented over the past 400 years. During the 19th century, Pettigrew emphasized that the heart was built on the basis of a modified blood vessel rather than in the form of skeletal muscles. This fact was reemphasized by Lev and Simkins as well as Grant in the 20th century, but the caveats listed by these authors have been ignored by proponents of two current concepts, which state either that the myocardium is arranged in the form of a "unique myocardial band," or that the walls of the ventricles are sequestrated in uniform fashion by laminar sheets of fibrous tissue extending from epicardium to endocardium. These two concepts are themselves incompatible and are further at variance with the majority of anatomic studies, which have emphasized the regional heterogeneity to be found in the three-dimensional packing of the myocytes within a supporting matrix of fibrous tissue. We reemphasize the significance of this three-dimensional muscular mesh, showing how the presence of intruding aggregates of myocytes extending in oblique transmural fashion also contends against the notion that all myocytes are orientated with their long axes parallel to the epicardial and enodcardial surfaces.