Many current food and health trends demand the use of more ecological, sustainable, and environmentally friendly techniques for the extraction of bioactive compounds, including antioxidants. However, extraction yields and final antioxidant activities vary between sources and are highly influenced by the given extraction method and nature and ratio of the employed solvent, especially for total polyphenols, flavonoids, and anthocyanins, which are well recognized as natural antioxidants with food applications. This review focused on the most common extraction techniques and potential antioxidant activity in the food industry for various natural antioxidant sources, such as green tea, rosemary, clove, and oregano. Green extraction techniques have been proven to be far more efficient, environmentally friendly, and economical. In general, these techniques include the use of microwaves, ultrasound, high hydrostatic pressure, pulsed electric fields, enzymes, and deep eutectic solvents, among others. These extraction methods are described here, including their advantages, disadvantages, and applications.