Plastics-based materials have a high carbon footprint, and their disposal is a considerable problem for the environment. Biodegradable bioplastics represent an alternative on which most countries have focused their attention to replace of conventional plastics in various sectors, among which food packaging is the most significant one. The evaluation of the optimal end-of-life process for bioplastic waste is of great importance for their sustainable use. In this review, the advantages and limits of different waste management routes—biodegradation, mechanical recycling and thermal degradation processes—are presented for the most common categories of biopolymers on the market, including starch-based bioplastics, PLA and PBAT. The analysis outlines that starch-based bioplastics, unless blended with other biopolymers, exhibit good biodegradation rates and are suitable for disposal by composting, while PLA and PBAT are incompatible with this process and require alternative strategies. The thermal degradation process is very promising for chemical recycling, enabling building blocks and the recovery of valuable chemicals from bioplastic waste, according to the principles of a sustainable and circular economy. Nevertheless, only a few articles have focused on this recycling process, highlighting the need for research to fully exploit the potentiality of this waste management route.