Due to the excellent properties of biodegradability and biocompatibility, aliphatic polycarbonate and polyesters are very promising either as biomaterials or as environmentally friendly materials to address growing ecological concerns. The first chapter describes an overview of ring-opening polymerization, enzymatic polymerization and their application on the polymerization of cyclic carbonate and lactones. The second chapter describes the synthesis of enantiomerically pure functional polycarbonate from a novel seven-membered-cyclic carbonate (5S, 6S)- Dimethyl 5,6- isopropylidene-1,3-dioxepin-2-one (ITC) derived from naturally occurring L-tartaric acid. The monomer was synthesized in three steps and screened for polymerization with four commercially available lipases. Block co-polymerization of ITC with ε-caprolactone in 'one-shot feeding' is reported in the third chapter. It is the first report of 'one-shot' block copolymerization of ε-caprolactone with a cyclic carbonate monomer. The deprotection of the ketal groups resulted in copolymers containing free hydroxy groups in the polymer backbone. In chapter four, star-shaped poly(ε-caprolactone)'s (PCL) series based on two tetra-hydroxy resorcinarenes initiators were reported. These polymers were synthesized by the ring-opening polymerization. The data suggest that the initiator core directed the PCL-arms toward more interactions resulting in increasing in the rigidity of star-polymers compare to linear-PCL.