Biodegradability makes aliphatic polyesters valuable candidates for biomaterials and environmentally friendly thermoplastics. Nevertheless, their chemical modification, which is mandatory for a series of potential applications, is usually a problem because it must be carried out under very mild conditions in order to prevent degradation by hydrolysis and/or transesterification from occurring. In this review, the copper(i) -catalyzed azide-alkyne cycloaddition, which is a click reaction, is shown to be very efficient to bypass these problems and to tailor the macromolecular architecture and functionality of those polyesters without facing undesired degradation reactions.