Polyurethanes and polycarbonates are widely used in a variety of applications including engineering, optical devices, and high-performance adhesives and coatings, etc., and are expected to find use also in the biomedical field owing to their biocompatibility and low toxicity. However, these polymers are currently produced using hazardous phosgene and isocyanates, which are derived from the reaction between an amine and phosgene. Extensive safety procedures are required to prevent exposure to phosgene and isocyanate because of its high toxicity. Therefore, the demand for the production of isocyanate-free polymers has now emerged. Among the alternative greener routes that have been proposed, a popular way is the ring-opening polymerization (ROP) of cyclic carbonate in bulk or solution, usually using metallic catalyst, metal-free initiator, or biocatalyst. This review presents the recent developments in the preparation and application of cyclic carbonates as monomers for ROP, with emphasis on phosgene- and isocyanate-free polymerization to produce aliphatic polycarbonates and polyurethanes and their copolymers.