The search for new biological sources of commercial value is a major goal for the sustainable management of natural resources. The huge amount of fishery by-catch or processing by-products continuously produced needs to be managed to avoid environmental problems and keep resource sustainability. Fishery by-products can represent an interesting source of high added value bioactive compounds, such as proteins, carbohydrates, collagen, polyunsaturated fatty acids, chitin, polyphenolic constituents, carotenoids, vitamins, alkaloids, tocopherols, tocotrienols, toxins; nevertheless, their biotechnological potential is still largely underutilized. Depending on their structural and functional characteristics, marine-derived biomolecules can find several applications in food industry, agriculture, biotechnological (chemical, industrial or environmental) fields. Fish internal organs are a rich and underexplored source of bioactive compounds; the fish gut microbiota biosynthesizes essential or short-chain fatty acids, vitamins, minerals or enzymes and is also a source of probiotic candidates, in turn producing bioactive compounds with antibiotic and biosurfactant/bioemulsifier activities. Chemical, enzymatic and/or microbial processing of fishery by-catch or processing by-products allows the production of different valuable bioactive compounds; to date, however, the lack of cost-effective extraction strategies so far has prevented their exploitation on a large scale. Standardization and optimization of extraction procedures are urgently required, as processing conditions can affect the qualitative and quantitative properties of these biomolecules. Valorization routes for such raw materials can provide a great additional value for companies involved in the field of bioprospecting. The present review aims at collecting current knowledge on fishery by-catch or by-products, exploring the valorization of their active biomolecules, in application of the circular economy paradigm applied to the fishery field. It will address specific issues from a biorefinery perspective: (i) fish tissues and organs as potential sources of metabolites, antibiotics and probiotics; (ii) screening for bioactive compounds; (iii) extraction processes and innovative technologies for purification and chemical characterization; (iv) energy production technologies for the exhausted biomass. We provide a general perspective on the techno-economic feasibility and the environmental footprint of the production process, as well as on the definition of legal constraints for the new products production and commercial use.