Plastics pollution is causing an environmental crisis, prompting development of new approaches for recycling and upcycling. Here we review challenges and opportunities in chemical and biological catalysis for plastics deconstruction, recycling, and upcycling. We stress the need for rigorous characterization and use of widely-available substrates, such that catalyst performance can be compared across studies. Where appropriate, we draw parallels between catalysis on biomass and plastics, as both substrates are low-value, solid, recalcitrant polymers. Innovations in catalyst design and process engineering are needed to overcome kinetic and thermodynamic limitations of plastics deconstruction. Chemical and biological catalysts will need to either act interfacially, where catalysts function at a solid surface, or polymers will need to be solubilized or processed to smaller intermediates to facilitate improved catalyst-substrate interaction. Overall, developing catalyst-driven technologies for plastics deconstruction and upcycling is critical to incentive improved plastics reclamation and reduce the severe, global burden of plastic waste.