Biodegradable polyesters are made by synthesizing copolymers derived from biodegradable hydroxyacid monomers as well as from hydroxyacid monomers containing a functional group such as an azide group, a halogen group, a thioacetate group, and the like. Preferably, the functionalized biodegradable polyester copolymers are derived from a functionalized hydroxyacid such as a homolog of lactic acid and/or glycolic acid with the copolyester thus containing functional groups on the backbone thereof. These biodegradable polyesters can be utilized wherever biodegradable polyesters are currently used, and also serve as a polymer to which various medical and drug delivery systems can be attached.