Consumers are now more concerned about food safety and hygiene following the COVID-19 pandemic. Antimicrobial packaging has attracted increased interest by reducing contamination of food surfaces to deliver quality and safe food while maintaining shelf life. Active packaging materials to reduce contamination or inhibit viral activity in packaged foods and on packaging surfaces are mostly prepared using solvent casting, but very few materials demonstrate antiviral activity on foods of animal origin, which are important in the human diet. Incorporation of silver nanoparticles, essential oils and natural plant extracts as antimicrobial agents in/on polymeric matrices provides improved antifungal, antibacterial and antiviral properties. This paper reviews recent developments in antifungal, antibacterial and antiviral packaging incorporating natural or synthetic compounds using preparation methods including extrusion, solvent casting and surface modification treatment for surface coating and their applications in several foods (i.e., bakery products, fruits and vegetables, meat and meat products, fish and seafood and milk and dairy foods). Findings showed that antimicrobial material as films, coated films, coating and pouches exhibited efficient antimicrobial activity in vitro but lower activity in real food systems. Antimicrobial activity depends on (i) polar or non-polar food components, (ii) interactions between antimicrobial compounds and the polymer materials and (iii) interactions between environmental conditions and active films (i.e., relative humidity, oxygen and water vapor permeability and temperature) that impact the migration or diffusion of active compounds in foods. Knowledge gained from the plethora of existing studies on antimicrobial polymers can be effectively utilized to develop multifunctional antimicrobial materials that can protect food products and packaging surfaces from SARS-CoV-2 contamination.