Fish processing by-products such as frames, trimmings, and viscera of commercial fish species are rich in proteins. Thus, they could potentially be an economical source of proteins that may be used to obtain bioactive peptides and functional protein hydrolysates for the food and nutraceutical industries. The structure, composition, and biological activities of peptides and hydrolysates depend on the freshness and the actual composition of the material. Peptides isolated from fishery by-products showed antioxidant activity. Changes in hydrolysis parameters changed the sequence and properties of the peptides and determined their physiological functions. The optimization of the value of such peptides and the production costs must be considered for each particular source of marine by-products and for their specific food applications. This review will discuss the functional properties of fishery by-products prepared using hydrolysis and their potential food applications. It also reviews the structure–activity relationships of the antioxidant activity of peptides as well as challenges to the use of fishery by-products for protein hydrolysate production.