Abstract Texture is one of the food quality attributes affecting the consumer's acceptability and the market value. Fish and shellfish undergo weakening or softening of muscle, particularly during extended storage under inappropriate conditions. The phenomenon is governed by endogenous proteases, both digestive and muscle proteases. Proteases present in the gastrointestinal tract that leach out to muscle tissue can induce proteolysis of myofibrillar and collagenous proteins. Furthermore, the muscle proteins present in gels fabricated from fish or shellfish meat also encounter degradation during thermal processing. Endogenous heat-activated proteases strongly bind to muscle proteins and are activated during heating, thereby degrading myofibrillar proteins, which are abundant in muscle tissue. This deterioration of the proteins directly leads to a weakened gel with poor water-holding capacity. Both cysteine and serine proteases are responsible for the degradation of myofibrillar proteins in several aquatic animals. Effective pretreatment of fish and shellfish, as well as the use of food-grade protease inhibitors (PIs), have been implemented to inactivate endogenous muscle and digestive proteases. For this review, proteolysis of muscle proteins and its control by food-grade PIs are revisited. Improved and effective lowering of proteolysis should be gained, thereby maintaining the quality of fish and their products.