Agricultural waste has been a prominent environmental concern due to its significant negative impact on the environment when it is incinerated, disposed of in landfills, or burned. These scenarios promoted innovations in the food packaging sector using renewable resources, namely agri-food waste and by-products such as bagasse, pulps, roots, shells, straws, and wastewater for the extraction and isolation of biopolymers that are later transformed into packaging materials such as bioplastics, biofilms, paper, and cardboards, among others. In this context, the circular bioeconomy (CBE) model is shown in the literature as a viable alternative for designing more sustainable production chains. Moreover, the biorefinery concept has been one of the main links between the agri-food chain and the food packaging industry. This review article aimed to compile recent advances in the food packaging field, presenting main industrial and scientific innovations, economic data, and the challenges the food packaging sector has faced in favor of sustainable development.