The harmful effects on the environment caused by the indiscriminate use of synthetic plastics and the inadequate management of post-consumer waste have given rise to efforts to redirect this consumption to bio-based economic models. In this sense, using biopolymers to produce materials is a reality for food packaging companies searching for technologies that allow these materials to compete with those from synthetic sources. This review paper focused on the recent trends in multilayer films with the perspective of using biopolymers and natural additives for application in food packaging. Firstly, the recent developments in the area were presented concisely. Then, the main biopolymers used (gelatin, chitosan, zein, polylactic acid) and main methods for multilayer film preparation were discussed, including the layer-by-layer, casting, compression, extrusion, and electrospinning methods. Furthermore, we highlighted the bioactive compounds and how they are inserted in the multilayer systems to form active biopolymeric food packaging. Furthermore, the advantages and drawbacks of multilayer packaging development are also discussed. Finally, the main trends and challenges in using multilayer systems are presented. Therefore, this review aims to bring updated information in an innovative approach to current research on food packaging materials, focusing on sustainable resources such as biopolymers and natural additives. In addition, it proposes viable production routes for improving the market competitiveness of biopolymer materials against synthetic materials.