Nowadays, the potato is one of the most cultivated and consumed food crops in the world and, in recent years, its production has experienced a sharp increase. Its industrial processing generates several by-products that are wasted and cause economic and environmental problems. Among them, potato peel stands out, representing up to 10% of the total potato residues obtained in the processing. On the other hand, these wastes, in addition to presenting antioxidant compounds, are rich in interesting chemical compounds of great value in a biorefinery model. This review summarizes the main compounds present in potato skins as well as the most used and innovative extraction methods employed for their isolation, with special emphasis on the fractions with biological activities. In addition, a sustainable biorefinery proposal focused on obtaining high added-value products with potential applications in the pharmaceutical, food, nutraceutical, or cosmetic industries is included.