Biomolecular recognition can be stubborn; changes in the structures of associating molecules, or the environments in which they associate, often yield compensating changes in enthalpies and entropies of binding, and no net change in affinities. This phenomenon—termed enthalpy/entropy (H/S) compensation—hinders efforts in biomolecular design, and its incidence—often a surprise to experimentalists—makes interactions between biomolecules difficult to predict. Although characterizing H/S compensation requires experimental care, it is unquestionably a real phenomenon that has, from an engineering perspective, useful physical origins. Studying H/S compensation can help illuminate the still-murky roles of water and dynamics in biomolecular recognition and self-assembly. This review summarizes known sources of H/S compensation (real and perceived) and lays out a conceptual framework for understanding and dissecting—and, perhaps, avoiding or exploiting—this phenomenon in biophysical systems.