The ring-opening copolymerization (ROCOP) of epoxides with CO2 or cyclic anhydrides is a versatile route toward synthesizing a wide range of polycarbonate and polyester copolymers. ROCOP most commonly uses binary catalyst systems comprising separate Lewis acid and nucleophilic cocatalyst components. However, the dependence on two discrete catalyst components leads to low activities at low loadings, and binary catalyst systems are prone to numerous side reactions. It was therefore proposed that covalently tethering the Lewis acid catalyst and cocatalyst together would increase both catalyst activity and selectivity in epoxide ROCOP. Since these initial efforts, many multifunctional catalysts featuring covalently tethered cationic or Lewis base cocatalyst(s) have been developed for epoxide ROCOP. This review examines multifunctional catalysts that have been developed for copolymerization of epoxides with CO2, cyclic anhydrides, carbonyl sulfide (COS), and cyclic thioanhydrides. In particular, we will assess how multifunctional catalysts' mechanisms of operations lead to improved activity and selectivity in ROCOP.