Every reader knows that an enzyme accelerates a reaction by reducing the activation-energy barrier. However, understanding how this is achieved by the structure of the enzyme and its interactions with stable complexes and transition states and, then, using this to (re)design enzymes to catalyze novel reactions remain the "holy grail" of mechanistic enzymology. The necessary foundation is the free-energy profile that specifies the energies of the bound substate, product, and intervening intermediates as well as the transition states by which they are interconverted. When this free-energy profile is compared to that for the uncatalyzed reaction, strategies for establishing and enhancing catalysis can be identified. This Perspective reminds readers that the first free-energy profile determined for an enzyme-catalyzed reaction, that for triosephosphate isomerase, was published in Biochemistry in 1976 by Jeremy R. Knowles, W. John Albery, and co-workers. They used the profile to propose three steps of increasing "subtlety" that can be influenced by evolutionary pressure to increase the flux through the reaction coordinate: (1) "uniform binding" of the substrate, product, and intermediates; (2) "differential binding" of complexes so that these are isoenergetic (to minimize the energy of the intervening transition states); and (3) "catalysis of an elementary step" in which the transition state for the kinetically significant chemical step is stabilized so that flux can be determined by the rate of substrate binding or product dissociation. These papers continue to guide mechanistic studies of enzyme-catalyzed reactions and provide principles for the (re)design of novel enzymes.