Natural bioactive compounds include a broad diversity of structures and functionalities that provide an excellent pool of molecules for the production of nutraceuticals, functional foods, and food additives. Some of those compounds can be found in nature at high concentration such as polyphenols but others can only be found at very low levels, so that massive harvesting is needed to obtain sufficient amounts, and their structural diversity and complexity make chemical synthesis unprofitable. The inherent difficulties in screening and producing these compounds have led to the development of advanced technologies. The commonly used methods for their extraction are the conventional liquid–liquid or solid–liquid extraction and the advanced include pressurized-liquid extraction, subcritical and supercritical extractions, and microwave- and ultrasound-assisted extractions. In addition, these extraction techniques have been improved with previous steps (enzyme-and instant controlled pressure drop-assisted extractions) which help to release the compounds from the matrix. These technologies could provide in the next few years an innovative approach to increase the production of specific compounds for use as nutraceuticals or as ingredients in the design of functional foods.