The increasing interest of consumers in functional foods has brought about a rise in demand for functional ingredients obtained using “natural” processes. In this review, new environmentally clean technologies for producing natural food ingredients are discussed. This work provides an updated overview on the principal applications of two clean processes, supercritical fluid extraction and subcritical water extraction, used to isolate natural products from different raw materials, such as plants, food by-products, algae and microalgae. Although the extraction of some compounds with antibacterial, antiviral or antifungical activity is discussed, special attention is paid to the extraction of antioxidant compounds, due to their important role in food preservation and health promotion.