Edible coatings, including green polymers are used frequently in the food industry to improve and preserve the quality of foods. Green polymers are defined as biodegradable polymers from biomass resources or synthetic routes and microbial origin that are formed by mono- or multilayer structures. They are used to improve the technological properties without compromising the food quality, even with the purpose of inhibiting lipid oxidation or reducing metmyoglobin formation in fresh meat, thereby contributing to the final sensory attributes of the food and meat products. Green polymers can also serve as nutrient-delivery carriers in meat and meat products. This review focuses on various types of bio-based biodegradable polymers and their preparation techniques and applications in meat preservation as a part of active and smart packaging. It also outlines the impact of biodegradable polymer films or coatings reinforced with fillers, either natural or synthesized, via the green route in enhancing the physicochemical, mechanical, antimicrobial, and antioxidant properties for extending shelf-life. The interaction of the package with meat contact surfaces and the advanced polymer composite sensors for meat toxicity detection are further considered and discussed. In addition, this review addresses the research gaps and challenges of the current packaging systems, including coatings where green polymers are used. Coatings from renewable resources are seen as an emerging technology that is worthy of further investigation toward sustainable packaging of food and meat products.