Green extraction techniques are more and more relevant due to major sustainable goals set by the United Nations. Greener extraction processes are being designed through the use of unconventional extraction techniques and green solvents, resulting in less hazardous processes which, consequently, reduces environmental impacts. This is also in line with the main principles of green chemistry. Additionally, greener extraction techniques intend to solve different drawbacks that are often related to conventional extraction techniques such as the high environmental impact. Biorefineries are a major player in developing greener extraction processes. These facilities take full advantage of several biomass sources, such as food waste, microalgae, and lignocellulosic biomass, in order to create high-value products, energy, alternative fuels, and bioactive compounds. Herein, a state-of-the-art review is presented, focused on presenting the greenest and least hazardous extraction processes that have been reported on the main biomass sources of a biorefinery—food waste, microalgae, and lignocellulosic biomass. Bioactive compounds such as phenolic compounds, bioactive pigments, and fatty acids are important in several sectors, mainly, the health, pharmaceutical, and agro-food sectors. Moreover, the bioactive compounds obtained through the aforementioned biomass sources and the different extraction procedures used will be presented and the authors will attempt to discuss, compare, and provide information about the most effective extraction techniques for each compound. Therewith, this review article should serve as a guide for industries, academics, and biorefineries in the future development of optimized and greener extraction procedures. Such analysis is lacking and could be very helpful for future research biorefinery projects since it tackles all of the major biomass sources of a biorefinery in a review article. To the best of our knowledge, this brings a novelty to the scientific community.