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.