The use of antibiotic growth promoters (AGP) in poultry production not only promotes the emergence of pathogenic multi-drug resistant bacteria, but it also compromises product quality, threatens animal and human health, and pollutes the environment. However, the complete withdrawal of AGP without alternatives could result in uncontrollable disease outbreaks that would jeopardize large-scale poultry intensification. Thus, the use of phytogenic products as potential alternatives to in-feed AGP has attracted worldwide research interest. These phytogenic products contain numerous biologically active substances with antioxidant and antimicrobial activities that can enhance poultry health, growth performance, and meat quality characteristics. In addition, the incorporation of phytogenic products as feed additives in poultry diets could result in the production of high-quality, drug-free, and organic poultry products that are safe for human consumption. Thus, this review examines the current evidence on the antioxidant and antimicrobial properties of a selection of phytogenic products, their effects on nutrient utilization, and physiological and meat quality parameters in poultry. The paper also reviews the factors that could limit the utilization of phytogenic products in poultry nutrition and proposes solutions that can deliver efficient and sustainable poultry production systems for global food and nutrition security.