The production of olive oil and wine are two of the main agri-food economic activities in Southern Europe. They generate large amounts of solid and liquid wastes (e.g., olive pomace, olive mill wastewater, grape pomace, grape stems, wine lees, and wine processing wastewater) that represent a major environmental problem. Consequently, the management of these residues has become a big challenge for these industries, since they are harmful to the environment but rich in bioactive compounds, such as polyphenols. In recent years, the recovery of phenolic compounds has been proposed as a smart strategy for the valorization of these by-products, from a circular economy perspective. This review aims to provide a comprehensive description of the state of the art of techniques available for the analysis, extraction, and purification of polyphenols from the olive mill and winery residues. Thus, the integration and implementation of these techniques could provide a sustainable solution to the olive oil and winery sectors.