Fish muscle, which accounts for 15%–25% of the total protein in fish, is a desirable protein source. Their hydrolysate is in high demand nutritionally as a functional food and thus has high potential added value. The hydrolysate contains physiologically active amino acids and various essential nutrients, the contents of which depend on the source of protein, protease, hydrolysis method, hydrolysis conditions, and degree of hydrolysis. Therefore, it can be utilized for various industrial applications including use in nutraceuticals and pharmaceuticals to help improve the health of humans. This review discusses muscle protein hydrolysates generated from the muscles of various fish species, as well as their amino acid composition, and highlights their functional properties and bioactivity. In addition, the role of the amino acid profile in regulating the biological and physiological activities, nutrition, and bitter taste of hydrolysates is discussed.