Combining CO2-chemistry with biomass conversion allows renewable polymeric materials including polycarbonates and polyhydroxyurethanes (PHUs) to be generated. The demand for robust materials with modular properties that can be prepared on an industrial scale is important and, to date, the most important polymeric materials are derived from petrochemicals. These materials inevitably result in CO2 emissions, and therefore making robust materials from renewable sources will contribute to a more sustainable society. An attractive way to address this challenge is to combine biomass transformations with CO2-fixation and material science. An identified target that combines all three aspects involves the preparation of PHUs (or non-isocyanate polyurethanes, NIPUs) via the polymerization of fully renewable cyclic carbonates derived from biomass and CO2 with a diamine compound that can also been derived from biomass sources. In this review, we critically analyze the progress in catalyst development for the efficient transformation of epoxides and CO2 to cyclic carbonates and polycarbonates. We also discuss the synthesis of PHUs from cyclic carbonates and diamines (not restricted to fully renewable compounds), including challenges in regiocontrol and biodegradability, as well as the role catalysts play in the synthesis of these polymers.