Sustainable polymers are materials derived from renewable, recycled and waste carbon resources and their combinations, which at the end of life can be recycled, biodegraded or composted. Sustainable polymers also exhibit reduced environmental impact throughout their life cycle. This Primer presents an overview of the research in and potential of sustainable polymers, with a focus on their life cycle, synthetic routes from renewable carbon feedstocks, production, material characterization, applications, end of life, data reproducibility and limitations faced, and provides a brief outlook. The Primer also briefly covers other carbon feedstocks such as carbon dioxide and wastes, including agricultural and woody residues. Although still in their infancy, new sustainable polymers are already finding applications in packaging, automotive parts and 3D printing. This Primer also discusses the headwinds facing the adoption of sustainable polymers, including complexities of recycling and composting, manufacturing scale-up, data reproducibility, deposition and potential solutions. Development of sustainable polymers will accelerate the age of sustainable polymers and create a truly circular economy for plastics by reducing production and use of virgin plastics from finite resources.