Whilst plastics have played an instrumental role in human development, growing environmental concerns have led to increasing public scrutiny and demands for outright bans. This has stimulated considerable research into renewable alternatives, and more recently, the development of alternative waste management strategies. Herein, we aim to highlight recent developments in the catalytic chemical recycling of two commercial polyesters, namely poly(lactic acid) (PLA) and poly(ethylene terephthalate) (PET). The concept of chemical recycling is first introduced, and associated opportunities/challenges are discussed within the context of the governing depolymerisation thermodynamics. Chemical recycling methods for PLA and PET are then discussed, with a particular focus on upcycling and the use of metal-based catalysts. Finally, our attention shifts to the emergence of new materials with the potential to modernise the plastics economy. Emerging opportunities and challenges are discussed within the context of industrial feasibility.