This overview addresses the remarkable efficiency of the mammalian heart as a pump of unique capacity to quickly vary output and ejection velocity and its relation to ventricular geometry, fiber architecture, integrity of collagen scaffold and microvasculature and appropriate electrical activation. The unique functional capacity of the ventricle depends critically on the organization of cardiac muscle fibers in layers of counter-wound helices encircling the ventricular cavity in a pattern that allows a special twisting motion during systole and early diastole, essential to the mechanical efficiency of the normal ventricle to eject and suction venous return. The important contribution of advances in imaging techniques is reviewed, especially magnetic resonance with tagging and tensor analysis to define fiber orientation; these measurements are made without the use of implanted devices that can distort structure and even impair function. The impact of loss of optimal fiber orientation and geometry of the ventricle as a result of diseases that cause heart failure is analyzed, along with the possibility of improvement by carefully planned surgical restoration of ventricular geometry. The very encouraging results yielded by these therapeutic strategies are critically dependent on a clear understanding of the relation of structure and function that our analysis attempts to promote. Simultaneously, there is full acknowledgment of the unanswered questions that are inevitable but equally essential to the continuing search that scientific progress depends on.