Petroleum-based packaging materials are typically nonbiodegradable, which leads to significant adverse environmental and health issues. Therefore, developing novel efficient, biodegradable, and nontoxic food packaging film materials has attracted increasing attention from researchers. Due to significant research and advanced technology, synthetic additives in packaging materials are progressively replaced with natural substances such as essential oils (EOs). EOs demonstrate favorable antioxidant and antibacterial properties, which would be an economical and effective alternative to synthetic additives. This review summarized the possible antioxidant and antimicrobial mechanisms of various EOs. We analyzed the properties and performance of food packaging films based on various biopolymers incorporated with EOs. The progress in intelligent packaging materials has been discussed as a prospect of food packaging materials. Finally, the current challenges regarding the practical application of EOs-containing biopolymer films in food packaging and areas of future research have been summarized.