Essential oils (EOs) have received attention in the food industry for developing biopolymer-derived food packaging materials. EOs are an excellent choice to replace petroleum-derived additives in food packaging materials due to their abundance in nature, eco-friendliness, and superior antimicrobial and antioxidant attributes. Thus far, EOs have been used in cellulose-, starch-, chitosan-, and protein-based food packaging materials. Biopolymer-based materials have lower antioxidant and antibacterial properties in comparison with their counterparts, and are not suitable for food packaging applications. Various synthetic-based compounds are being used to improve the antimicrobial and antioxidant properties of biopolymers. However, natural essential oils are sustainable and non-harmful alternatives to synthetic antimicrobial and antioxidant agents for use in biopolymer-derived food packaging materials. The incorporation of EOs into the polymeric matrix affects their physicochemical properties, particularly improving their antimicrobial and antioxidant properties. EOs in the food packaging materials increase the shelf life of the packaged food, inhibit the growth of microorganisms, and provide protection against oxidation. Essential oils also influence other properties, such as tensile, barrier, and optical properties of the biopolymers. This review article gives a detailed overview of the use of EOs in biopolymer-derived food packaging materials. The innovative ways of incorporating of EOs into food packaging materials are also highlighted, and future perspectives are discussed.