Polymers (plastics) have transformed our lives by providing access to inexpensive and versatile materials with a variety of useful properties. While polymers have improved our lives in many ways, their longevity has created some unintended consequences. The extreme stability and durability of most commercial polymers, combined with the lack of equivalent degradable alternatives and ineffective collection and recycling policies, have led to an accumulation of polymers in landfills and oceans. This problem is reaching a critical threat to the environment, creating a demand for immediate action. Chemical recycling and upcycling involve the conversion of polymer materials into their original monomers, fuels or chemical precursors for value-added products. These approaches are the most promising for value-recovery of post-consumer polymer products; however, they are often cost-prohibitive in comparison to current recycling and disposal methods. Catalysts can be used to accelerate and improve product selectivity for chemical recycling and upcycling of polymers. This review aims to not only highlight and describe the tremendous efforts towards the development of improved catalysts for well-known chemical recycling processes, but also identify new promising methods for catalytic recycling or upcycling of the most abundant commercial polymers.