A critical goal of metabolism in living cells is the synthesis of adenosine triphosphate (ATP). ATP is synthesized by the enzyme F1F0-ATP synthase. This enzyme, the smallest-known molecular machine, couples proton translocation through its membrane-embedded, hydrophobic domain, F0, to the synthesis of ATP from adenosine diphosphate (ADP) and inorganic phosphate (Pi) in its soluble, hydrophilic headpiece, F1. Animals, plants and microorganisms all capture and utilize energy by this important chemical reaction. How does it occur? The binding change mechanism and the torsional mechanism of energy transduction and ATP synthesis are two mechanisms that have been proposed in the literature. According to the binding change mechanism (which considers reversible catalysis and site-site cooperativity), energy is required primarily for release of synthesized ATP, but not for its synthesis. On the other hand, according to the torsional mechanism (which considers an irreversible mode of catalysis and absence of cooperativity), all the elementary steps require energy, and the ion-protein interaction energy obtained from the ion gradients is used to synthesize ATP, for Pi binding, and for straining the beta-epsilon bond in order to enable ADP to bind. The energy to release preformed ATP from the tight catalytic site (betaDP) is provided by the formation of the beta-epsilon ester linkage. First, the central features of these mechanisms are clearly delineated. Then, a critical scrutiny of these mechanisms is undertaken. The predictions of the torsional mechanism are listed. In particular, how the torsional mechanism deals with the specific difficulties associated with other mechanisms, and how it seeks to explain a wealth of structural, spectroscopic, and biochemical data is discussed in detail. Recent experimental data in support of the mechanism are presented. Finally, in view of the molecular machine nature of energy transduction, the indispensability of applying engineering tools at the molecular level is highlighted. This paves the way for the development of a new field: Molecular Physiological Engineering.