Rising global populations and enhanced standards of living in so-called developing countries have led to an increased demand of food, in particular meat, worldwide. While increasing the production of broiler meat could be a potential solution to this problem, broiler meat is plagued by health concerns, such as the development of antimicrobial resistance and lower meat quality. For this reason, the supplementation of poultry feed with vitamins and antioxidant compounds, such as polyphenols, has become an attractive prospect for research in this sector. Such supplements could be obtained by extraction of agricultural byproducts (in particular, grape pomaces and artichoke leaves and bracts), thus contributing to reductions in the total amount of waste biomass produced by the agricultural industry. In this review, the effects of poultry feed supplementation with bioactive extracts from grape pomace (skins and/or seeds), as well as extracts from artichoke leaves and bracts, were explored. Moreover, the various methods that have been employed to obtain extracts from these and other agricultural byproducts were listed and described, with a particular focus on novel, eco-friendly extraction methods (using, for example, innovative and biocompatible solvents like Deep Eutectic Solvents (DESs)) that could reduce the costs and energy consumption of these procedures, with similar or higher yields compared to standard methods.