The present invention relates to methods of synthesizing long-chain polyunsaturated fatty acids, especially eicosapentaenoic acid, docosapentaenoic acid and docosahexaenoic acid, in recombinant cells such as yeast or plant cells. Also provided are recombinant cells or plants which produce long-chain polyunsaturated fatty acids. Furthermore, the present invention relates to a group of new enzymes which possess desaturase or elongase activity that can be used in methods of synthesizing long-chain poly unsaturated fatty acids.