Progress in catalytic polymerization of olefins and cycloolefins with late-transition metal complexes as catalysts,involving iron,cobalt,nickel and palladium complexes of coordinating diimine, coordinating salicylaldimine and , phosphine-hybridy ligands are reviewed.The effect of ligand on activity and the polymer structure are discussed.It is pointed out that the catalytic polymerization of ethylene with cycloolefins is the hotspot in this field.