Recently, academic research and industries have gained awareness about the economic, environmental, and social impacts of conventional plastic packaging and its disposal. This consciousness has oriented efforts towards more sustainable materials such as biopolymers, paving the way for the “green era” of food packaging. This review provides a schematic overview about polymers and blends of them, which are emerging as promising alternatives to conventional plastics. Focus was dedicated to biopolymers from renewable sources and their applications to produce sustainable, active packaging with antimicrobial and antioxidant properties. In particular, the incorporation of plant extracts, food-waste derivatives, and nano-sized materials to produce bio-based active packaging with enhanced technical performances was investigated. According to recent studies, bio-based active packaging enriched with natural-based compounds has the potential to replace petroleum-derived materials. Based on molecular composition, the natural compounds can diversely interact with the native structure of the packaging materials, modulating their barriers, optical and mechanical performances, and conferring them antioxidant and antimicrobial properties. Overall, the recent academic findings could lead to a breakthrough in the field of food packaging, opening the gates to a new generation of packaging solutions which will be sustainable, customised, and green.