Using catalyst system as the mainline, recent advances about chemical and enzymatic preparation of epoxy fatty acid methyl ester（EFAMEs） in different catalyst systems were reviewed. The advantages and disadvantages of heteropolyacid, ionic liquid and enzyme catalysis were compared.The effects of oxygen carriers, substrate mole ratio, H2O2 adding modes, reaction temperature on FAMEs epoxidation were discussed in enzyme catalyst system.The immobilized technique of lipase and the existing  problems were analyzed.It was pointed out that finding the right carrier solid load lipase,improving the activity of lipase,searching for suitable epoxidation process conditions and improving the utilization rate of lipase would be the development directions.