Society and consumers are increasingly concerned about food safety and the sustainability of food production systems. A significant amount of by-products and discards are generated during the processing of aquatic animals, which still needs to be fully utilized by the food industry. The management and sustainable use of these resources are essential to avoiding environmental pollution and resource waste. These by-products are rich in biologically active proteins, which can be converted into peptides by enzymatic hydrolysis or fermentation treatment. Therefore, exploring the extraction of collagen peptides from these by-products using an enzymatic hydrolysis technology has attracted a wide range of attention from numerous researchers. Collagen peptides have been found to possess multiple biological activities, including antioxidant, anticancer, antitumor, hypotensive, hypoglycemic, and anti-inflammatory properties. These properties can enhance the physiological functions of organisms and make collagen peptides useful as ingredients in food, pharmaceuticals, or cosmetics. This paper reviews the general methods for extracting collagen peptides from various processing by-products of aquatic animals, including fish skin, scales, bones, and offal. It also summarizes the functional activities of collagen peptides as well as their applications.