The wine industry generates substantial quantities of by-products, including grape pomace, seeds, skins, stems, wine lees, and wastewater, which are valuable sources of polyphenols, dietary fibers, lipids, proteins, and other bioactive compounds. This review examines the composition, extraction, and valorization of winery residues within a circular bioeconomy framework, with particular emphasis on the distribution and recovery of major polyphenols, including flavonoids, phenolic acids, stilbenes, anthocyanins, and tannins. Conventional extraction methods are critically compared with emerging green technologies, including ultrasound- and microwave-assisted extraction, pulsed electric fields, high-voltage electrical discharges, supercritical fluid extraction, and pressurized liquid extraction, considering their efficiency, sustainability, scalability, and industrial potential. The valorization of winery-derived ingredients in functional foods, edible packaging, nutraceuticals, cosmetics, animal feed, biofuels, and other value-added products is also discussed. Despite significant progress, raw material variability, process standardization, techno-economic feasibility, regulatory compliance, and consumer acceptance remain major barriers to industrial implementation. Integrating green extraction technologies with biorefinery approaches, life-cycle assessment, and process optimization could enhance resource efficiency and product quality, supporting the transition toward a more sustainable and circular wine industry.