Polyesters synthesized through the alternating copolymerization of epoxides and cyclic anhydrides compose a growing class of polymers that exhibit an impressive array of chemical and physical properties. Because they are synthesized through the chain-growth polymerization of two variable monomers, their syntheses can be controlled by discrete metal complexes, and the resulting materials vary widely in their functionality and physical properties. This polymer-focused review gives a perspective on the current state of the field of epoxide/anhydride copolymerization mediated by discrete catalysts and the relationships between the structures and properties of these polyesters.