Color is one of the main sensory properties in the food industry. Currently, there is a global interest to replace synthetic colorants with natural compounds. In line with this, many plants have been shown to serve as sources of natural pigments. Elucidation of their chemical structures has allowed the identification of several compounds such as carotenoids, chlorophyll, betalains, anthocyanins, and flavonoids, whose popularity has increased due to the health benefits associated with their consumption. One of the most important steps in the production and extraction of plant-derived pigments is extraction. Soxhlet extraction, maceration, and carbon dioxide extraction are conventional methods that have been widely used at the laboratory, pilot, and industrial scales for this purpose. However, in the last years, several nonconventional methods, such as ultrasound- and microwave-assisted extraction, high pressure, supercritical fluid extraction, and electric and pulsed electric field extraction, have emerged as alternatives to conventional methods aimed to reduce the use of organic solvents and extraction time, without being harmful to the environment. In this study, the classification and extraction of plant-derived pigments, their economic importance, trends, and challenges for their use and extraction in the food industry are reviewed.