Drastic growth in the amount of global food waste produced is observed every year, not only due to incessant population growth but also economic growth, lifestyle, and diet changes. As a result of their increasing health awareness, people are focusing more on healthy diets rich in fruits and vegetables. Thus, following worldwide fruit and vegetable consumption and their processing in various industries (juice, jams, wines, preserves), significant quantities of agro-industrial waste are produced (pomace, peels, seeds) that still contain high concentrations of bioactive compounds. Among bioactive compounds, anthocyanins have an important place, with their multiple beneficial effects on health; therefore, their extraction and recovery from food waste have become a topic of interest in recent years. Accordingly, this review aims to summarize the primary sources of anthocyanins from food waste and the novel eco-friendly extraction methods, such as pulsed electric field extraction, enzyme-assisted extraction, supercritical fluid extraction, pressurized liquid extraction, microwave-assisted extraction, and ultrasonic-assisted extraction. The advantages and disadvantages of these techniques will also be covered to encourage future studies and opportunities focusing on improving these extraction techniques.