The biotechnological applications of enzymes are limited due to the activity-stability trade-off, which implies that an increase in activity is accompanied by a concomitant decrease in protein stability. This premise is based on thermally adapted homologous enzymes where cold-adapted enzymes show high intrinsic activity linked to enhanced thermolability. In contrast, thermophilic enzymes show low activity around ambient temperatures. Nevertheless, genetically and chemically modified enzymes are beginning to show that the activity-stability trade-off can be overcome. In this review, the origin of the activity-stability trade-off, the thermodynamic basis for enhanced activity and stability, and various approaches for escaping the activity-stability trade-off are discussed. The role of entropy in enhancing both the activity and the stability of enzymes is highlighted with a special emphasis placed on the involvement of solvent water molecules. This review is concluded with suggestions for further research, which underscores the implications of these findings in the context of productivity curves, the Daniel-Danson equilibrium model, catalytic antibodies, and life on cold planets.