With the increase in the world population, the overexploitation of the planet’s natural resources is becoming a worldwide concern. Changes in the way humankind thinks about production and consumption must be undertaken to protect our planet and our way of living. For this change to occur, sustainable development together with a circular economic approach and responsible consumption are key points. Agriculture activities are responsible for more than 10% of the greenhouse gas emissions; moreover, by 2050, it is expected that food production will increase by 60%. The valorization of food waste is therefore of high importance to decrease the environmental footprint of agricultural activities. Fruits and vegetables are wildly consumed worldwide, and grapes are one of the main producers of greenhouse gases. Grape biomass is rich in bioactive compounds that can be used for the food, pharmaceutical and cosmetic industries, and their extraction from this food residue has been the target of several studies. Among the extraction techniques used for the recovery of bioactive compounds from food waste, subcritical water extraction (SWE) has been the least explored. SWE has several advantages over other extraction techniques such as microwave and ultrasound extraction, allowing high yields with the use of only water as the solvent. Therefore, it can be considered a green extraction method following two of the principles of green chemistry: the use of less hazardous synthesis (principle number 3) and the use of safer solvents and auxiliaries (principle number 5). In addition, two of the green extraction principles for natural products are also followed: the use of alternative solvents or water (principle number 2) and the use of a reduced, robust, controlled and safe unit operation (principle number 5). This review is an overview of the extraction process using the SWE of grape biomass in a perspective of the circular economy through valorization of the bioactive compounds extracted. Future perspectives applied to the SWE are also discussed, as well as its ability to be a green extraction technique.