The wine industry is one of the most relevant socio-economic activities in Europe. However, this industry represents a growing problem with negative effects on the environment since it produces large quantities of residues that need appropriate valorization or management. From the perspective of biorefinery and circular economy, the winery residues show high potential to be used for the formulation of new products. Due to the substantial quantities of phenolic compounds, flavonoids, and anthocyanins with high antioxidant potential in their matrix, these residues can be exploited by extracting bioactive compounds before using the remaining biomass for energy purposes or for producing fertilizers. Currently, there is an emphasis on the use of new and greener technologies in order to recover bioactive molecules from solid and liquid winery residues. Once the bio compounds are recovered, the remaining residues can be used for the production of energy through bioprocesses (biogas, bioethanol, bio-oil), thermal processes (pyrolysis, gasification combustion), or biofertilizers (compost), according to the biorefinery concept. This review mainly focuses on the discussion of the feasibility of the application of the biorefinery concept for winery residues. The transition from the lab-scale to the industrial-scale of the different technologies is still lacking and urgent in this sector.