Current trends in Analytical Chemistry are focused on the development of more sustainable and environmentally friendly procedures. However, and despite technological advances at the instrumental level having played a very important role in the greenness of the new methods, there is still work to be done regarding the sample preparation stage. In this sense, the implementation of new materials and solvents has been a great step towards the development of “greener” analytical methodologies. In particular, the application of deep eutectic solvents (DESs) has aroused great interest in recent years in this regard, as a consequence of their excellent physicochemical properties, general low toxicity, and high biodegradability if they are compared with classical organic solvents. Furthermore, the inclusion of DESs based on natural products (natural DESs, NADESs) has led to a notable increase in the popularity of this new generation of solvents in extraction techniques. This review article focuses on providing an overview of the applications and limitations of DESs in solvent-based extraction techniques for food analysis, paying especial attention to their hydrophobic or hydrophilic nature, which is one of the main factors affecting the extraction procedure, becoming even more important when such complex matrices are studied.