Biodegradable and biocompatible aliphatic polyesters have a great potential as biomaterials and environmentally friendly thermoplastics. An intensive research effort has been devoted to living or at least controlled ring opening polymerization (ROP) of lactones, lactides, and glycolides that contributes enormously to macromolecular engineering of these aliphatic polyesters. The recent progress in the field has been reviewed and discussed in terms of structure/nature of the polymerization promoters. A first section focuses on organometallic initiators and catalysts, with emphasis on the more efficient aluminum, tin, and yttrium alkoxides. Special attention is also paid to the steroselective ROP of
D
,
L
‐ and
meso
‐lactide into polylactide of controlled tacticity. Contamination of the final polyesters by metallic residues is a drawback, which is now tackled by grafting metal alkoxides onto solid supports. The second section is dedicated to ROP mediated by enzymes, which is a very attractive strategy. Finally, “all organic” processes have been recently worked out, which are very promising for the synthesis of aliphatic polyesters free from any metallic contaminants.