The winemaking sector is one of the most productive worldwide, and thus it also generates large amounts of by-products with high environmental impacts. Furthermore, global market trends and government regulations promote industrial alternatives based on sustainable production processes. As a result, several studies have focused their attention on the reuse of grape by-products in the agro-food chain. Vine shoots, grape stalks, and wine lees, although produced to a lesser extent than grape pomace, have increasingly been receiving attention for their applications in the food sector, since they are a good source of functional and bioactive compounds. In this framework, our review highlights the promising results obtained by exploiting the antioxidant and/or antimicrobial activity of vine shoots, grape stalks, and wine lees or their extracts to replace the most common oenological additives and to assay the activity against food pathogens. Further, innovative functional foods and sustainable food packaging have been formulated by taking advantage of polyphenols and fiber, as well as plant bio-stimulants, in order to obtain grapes and wines with high quality characteristics. Overall, these by-products showed the potential to be recycled into the food chain as functional additives for different products and applications, supporting the sustainability of the winemaking sector.