Aliphatic polyesters are among the most important class of synthetic polymers for biomedical applications due to their biodegradability and generally high biocompatibility. However, conventional aliphatic polyesters are semi-crystalline, hydrophobic solids lacking in functionality, such that strategic tailoring of their structure and functionality could expand their application base considerably. Numeorus synthetic methods have been examined for introducing functionality to aliphatic polyesters. This chapter will describe a number of reported methods, focusing on examples of ring-opening polymerization (ROP) of functionalized lactones, and post-polymerization functionalization that affords well-defined materials with high degrees of functionality and narrow polydispersities. In addition, new developments in biocompatible ROP catalysts as well as novel polyester architectures, such as cyclic polymers, will be discussed.