The absence of trace amounts of natural bioactive compounds with important biological activities in traditional dietary models for global farm animals, coupled with an incomplete theoretical system for animal nutrition, has led to unbalanced and inadequate animal nutrition. This deficiency has adversely impacted animal health and the ecological environment, presenting formidable challenges to the advancement of the swine breeding industry in various countries around the world toward high-quality development. Recently, due to the ban of antibiotics for growth promotion in swine diets, botanical active compounds have been extensively investigated as feed additives. Polyphenols represent a broad group of plant secondary metabolites. They are natural, non-toxic, pollution-free, and highly reproducible compounds that have a wide range of physiological functions, such as antioxidant, anti-inflammatory, immunomodulatory, antiviral, antibacterial, and metabolic activities. Accordingly, polyphenols have been widely studied and used as feed additives in swine production. This review summarizes the structural characteristics, classification, current application situation, general properties of polyphenols, and the latest research advances on their use in swine production. Additionally, the research and application bottlenecks and future development of plant polyphenols in the animal feed industry are reviewed and prospected. This review aims to stimulate the in-depth study of natural plant polyphenols and the research and development of related products in order to promote the green, healthy, and high-quality development of swine production, while also providing ideas for the innovation and development in the theoretical system of animal nutrition.