Meat is known for its high perishability and short shelf life if not properly packaged or stored. Packaging materials play a crucial role in preserving food quality, and there is a growing demand from consumers, industry professionals, and researchers for natural packaging materials that incorporate health-beneficial extracts. Additionally, there is an increasing emphasis on avoiding non-biodegradable plastics in order to reduce environmental pollution. Currently used polymers in food packaging typically feature properties such as oxygen barriers, moisture resistance, and oxidation inhibition, helping to prevent undesirable aromas, flavors, and colors in food. Packaging not only serves as a container for transportation but also prevents physical damage, maintains quality, and ensures food safety. In the pursuit of more sustainable solutions, various compounds are being explored for food packaging, including those derived from proteins, lipids, waxes, and polysaccharides. These materials can be combined with bioactive compounds, such as natural plant extracts, which provide antioxidant, antimicrobial, anti-inflammatory, and anticancer benefits. Different techniques, such as electrohydrodynamic processes and casting methods, are employed in the preparation of these packaging materials. This review highlights the applications and properties of polymers used in meat packaging and promotes the use of biodegradable materials as a viable solution to reduce environmental pollution.