What makes living things special is how they manage matter, energy, and entropy. A general theory of organismal metabolism should therefore be quantified in these three currencies while capturing the unique way they flow between individuals and their environments. We argue that such a theory has quietly arrived -- 'Dynamic Energy Budget' (DEB) theory -- which conceptualises organisms as a series of macrochemical reactions that use energy to transform food into structured biomass and bioproducts while producing entropy. We show that such conceptualisation is deeply rooted in thermodynamic principles and that, with the help of a small set of biological assumptions, it underpins the emergence of fundamental ecophysiological phenomena, most notably the three-quarter power scaling of metabolism. Building on the subcellular nature of the theory, we unveil the eco-evolutionary relevance of coarse-graining biomass into qualitatively distinct, stoichiometricially fixed pools with implicitly regulated dynamics based on surface area-volume relations. We also show how generalised enzymes called 'synthesising units' and an information-based state variable called 'maturity' capture transitions between ecological and physiological metabolic interactions, and thereby transitions between unicellular and multicellular metabolic organisation. Formal theoretical frameworks make the constraints imposed by the laws of nature explicit, which in turn leads to better research hypotheses and avoids errors in reasoning. DEB theory uniquely applies thermodynamic formalism to organismal metabolism, linking biological processes across different scales through the transformation of matter and energy, the production of entropy, and the exchange of information. We propose ways in which the theory can inform trans-disciplinary efforts at the frontiers of the life sciences.