Seafood by-products, produced by a range of different organisms, such as fishes, shellfishes, squids, and bivalves, are usually discarded as wastes, despite their possible use for innovative formulations of functional foods. Considering that “wastes” of industrial processing represent up to 75% of the whole organisms, the loss of profit may be coupled with the loss of ecological sustainability, due to the scarce recycling of natural resources. Fish head, viscera, skin, bones, scales, as well as exoskeletons, pens, ink, and clam shells can be considered as useful wastes, in various weight percentages, according to the considered species and taxa. Besides several protein sources, still underexploited, the most interesting applications of fisheries and aquaculture by-products are foreseen in the biotechnological field. In fact, by-products obtained from marine sources may supply bioactive molecules, such as collagen, peptides, polyunsaturated fatty acids, antioxidant compounds, and chitin, as well as catalysts in biodiesel synthesis. In addition, those sources can be processed via chemical procedures, enzymatic and fermentation technologies, and chemical modifications, to obtain compounds with antioxidant, anti-microbial, anti-cancer, anti-hypertensive, anti-diabetic, and anti-coagulant effects. Here, we review the main discards from fishery and aquaculture practices and analyse several bioactive compounds isolated from seafood by-products. In particular, we focus on the possible valorisation of seafood and their by-products, which represent a source of biomolecules, useful for the sustainable production of high-value nutraceutical compounds in our circular economy era.