At a time when food safety awareness is increasing, attention is paid not only to food and additives but also to packaging materials. Most current food packaging is usually made of traditional petroleum-based polymeric materials, which are not biodegradable and have adverse effects on the environment and health. In this context, the development of new non-toxic and biodegradable materials for extending the best-before date of food is receiving increasing attention. In addition, additives in packaging materials may migrate outward, resulting in contact with food. For this reason, additives are also seen as a transition from synthetic additives to natural extracts. Active extracts from animals and plants having good antioxidant and antibacterial properties are also beneficial for human health. It is indisputable that active extracts are ideal substitutes for synthetic additives. Polymer packaging materials combined with active extracts not only maintain their original mechanical and optical properties and thermal stability but also endow polymers with new functions to extend the shelf life of food. This review paper provides an overview of this promising natural extract-containing polymer-based active packaging, with a focus on plant essential oils (containing phenolics, monoterpenes, terpene alcohols, terpene ketones, and aldehydes), pigments (procyanidins), vitamins (vitamin B), and peptides (nisin). In particular, this paper covers the research progress of such active extracts, in single or compound forms, combined with diverse polymers (mostly biopolymers) for food packaging applications with particular focus on the antioxidant and antibacterial properties of packaging materials.