Aliphatic polyesters prepared by ring-opening polymerization of lactones are now used worldwide as bioresorbabale devices in surgery (orthopaedic devices, sutures, stents, tissue engineering, and adhesion barriers) and in pharmacology (control drug delivery). This review presents the various methods of the synthesis of polyesters and tailoring the properties by proper control of molecular weight, composition, and architecture so as to meet the stringent requirements of devices in the medical field. The effect of structure on properties and degradation has been discussed. The applications of these polymers in the biomedical field are described in detail.