Large amounts of food waste are produced each year. These residues require appropriate management to reduce their environmental impact and, at the same time, economic loss. However, this waste is still rich in compounds (e.g., colorants, antioxidants, polyphenols, fatty acids, vitamins, and proteins) that can find potential applications in food, pharmaceutical, and cosmetic industries. Conventional extraction techniques suffer some drawbacks when applied to the exploitation of food residues, including large amounts of polluting solvents, increased time of extraction, possible degradation of the active molecules during extraction, low yields, and reduced extraction selectivity. For these reasons, advanced extraction techniques have emerged in order to obtain efficient residue exploitation using more sustainable processes. In particular, performing extraction under high-pressure conditions, such as supercritical fluids and pressurized liquid extraction, offers several advantages for the extraction of bioactive molecules. These include the reduced use of toxic solvents, reduced extraction time, high selectivity, and the possibility of being applied in combination in a cascade of progressive extractions. In this review, an overview of high-pressure extraction techniques related to the recovery of high added value compounds from waste generated in food industries is presented and a critical discussion of the advantages and disadvantages of each process is reported. Furthermore, the possibility of combined multi-stage extractions, as well as economic and environmental aspects, are discussed in order to provide a complete overview of the topic.