The replacement of current petroleum-based plastics with sustainable alternatives is a crucial but formidable challenge for the modern society. Catalysis presents an enabling tool to facilitate the development of sustainable polymers. This review provides a system-level analysis of sustainable polymers and outlines key criteria with respect to the feedstocks the polymers are derived from, the manner in which the polymers are generated, and the end-of-use options. Specifically, we define sustainable polymers as a class of materials that are derived from renewable feedstocks and exhibit closed-loop life cycles. Among potential candidates, aliphatic polyesters and polycarbonates are promising materials due to their renewable resources and excellent biodegradability. The development of renewable monomers, the versatile synthetic routes to convert these monomers to polyesters and polycarbonate, and the different end-of-use options for these polymers are critically reviewed, with a focus on recent advances in catalytic transformations that lower the technological barriers for developing more sustainable replacements for petroleum-based plastics.