Controlled routes to prepare polyesters and polycarbonates are of interest due to the widespread application of these materials and the opportunities provided to prepare new copolymers. Furthermore, ring-opening copolymerization may enable new poly(ester-carbonate) materials to be prepared which are inaccessible using alternative polymerizations. This review highlights recent advances in the ring-opening copolymerization catalysis, using epoxides coupled with anhydrides or CO2, to produce polyesters and polycarbonates. In particular, the structures and performances of various homogeneous catalysts are presented for the epoxide-anhydride copolymerization. The properties of the resultant polyesters and polycarbonates are presented and future opportunities highlighted for developments of both the materials and catalysts.