Compared with widely used polyolefin materials, aliphatic polyesters can show the same properties, and their unique biocompatibility and degradability make them widely used in electronics, absorbable surgical suture, food packaging, biomedicine and so on. They have become an environmentally friendly substitute for traditional polyolefin plastics, especially aliphatic polyester materials derived from biomass. Ring opening polymerization (ROP) is the main method for synthesizing aliphatic polyester at present. Aiming at the application of catalytic ring opening polymerization in the synthesis of aliphatic polyester, this paper summarizes two main catalytic systems involved in this field, namely metal based catalyst and metal free organic catalyst, and gives a preliminary introduction to the emerging enzyme catalytic system. This paper lists the chemical structures of relevant important catalytic systems, aims to reveal the catalytic reaction characteristics of various systems, and focuses on and comments on the effects of catalyst structure on catalytic efficiency, controllability, molecular weight and stereoselectivity. Specifically, metal based catalysts mainly include complexes formed by the coordination of central metal with N-heterocyclic carbene and thiourea, which have great adjustability in structure, and different structures can be selected according to the needs of catalysis; Metal free organic catalysts such as organic base catalysts (phosphonitrile base, N-heterocyclic carbene, etc.) and organic acid catalysts (phosphoric acid, squaric acid, etc.) often have the advantages of high catalytic efficiency, molar mass control and stereoselectivity. In addition, lipase catalyst has the characteristics of wide reaction range, mild reaction and no metal pollution residue. [GRAPHICS]