Human health, food spoilage, and plastic waste, which are three great topical concerns, intersect in the field of food packaging. This has created a trend to replace synthetic food preservatives with natural ones, to produce bio-functional food packaging, and to shift towards biodegradable polymeric materials. Among the natural bioactive agents, essential oils are gaining more and more attention in food packaging applications due to their various benefits and fewer side-effects. However, their volatility, hydrophobicity, and strong odor and taste limit the direct use in food-related applications. Fixation into polymeric matrices represents a suitable strategy to promote the benefits and reduce the drawbacks. Emulsification and electrospinning are largely used techniques for protection and stabilization of essential oils. These methods offer various advantages in active food packaging, such as controlled release, ensuring long-term performance, decreased amounts of active agents that gain enhanced functionality through increased available surface area in contact with food, and versatility in packaging design. This review focuses on creating correlations between the use of essential oils as natural additives, stabilization methods, and biodegradable polymeric matrices or substrates in developing bioactive food packaging materials. Documentation was performed via the Scopus, ScienceDirect, and PubMed databases, selecting the publications after the year 2018. Particular attention was given to the publications that tested materials on food/food pathogens to evaluate their performances in retarding spoilage. Research gaps were also identified on the topic, materials being tested mainly at short time after preparation without considering the long-term storage that usually occurs in actual practice between production and use, and insufficient research related to upscaling.