Abstract: It is an emerging method to synthesize polymers via organocatalysts in very recent years. More attention has been paid to the organocatalytic ring-opening copolymerization of cyclic ethers (epoxides) with cyclic anhydrides since that these monomers are abundant and most of organocatalysts are low toxic and non-sensitive to oxygen and moisture. Thus, the organocatalytic copolymerization of epoxides with cyclic anhydrides is very promising and has a wide application prospect. In this review, the types of organocatalysts, cyclic ethers (epoxides) and anhydrides are systematically presented with detail discussion. The typical copolymerization and related mechanism are intensively discussed. Of special, the activity of the Lewis pairs consisted of the organoboron compounds and onium salts are comparable to the counterparts of metal organic catalysts, which means that the organocatalysts have a great potential in synthesizing polyesters. A synthetic strategy is proposed to utilize neutral organic molecules (i.e., Lewis acids) to introduce the steric and electronic effect for the growing anions for controlled copolymerization of epoxides and cyclic anhydrides. The future mission in this field is to develop highly active organocatalysts for the living copolymerization of epoxides with cyclic anhydrides for making polyesters with perfect selectivity (including chemoselectivity, regioselectivity and stereoselectivity).