Abstract <p>The demand for sustainable and eco-friendly alternatives to fossil and plant oil-derived chemicals has spurred interest in microbial production of lipids, particularly triacylglycerols, fatty acids, and their derivatives. Yeasts are promising platforms for synthesizing these compounds due to their high lipid accumulation capabilities, robust growth, and <i>g</i>enerally <i>r</i>ecognized <i>a</i>s <i>s</i>afe (GRAS) status. There is vast interest in fatty acid and triacylglycerol products with tailored fatty acid chain lengths and compositions, such as polyunsaturated fatty acids and substitutes for cocoa butter and palm oil. However, microbes naturally produce a limited set of mostly long-chain fatty acids, necessitating the development of microbial cell factories with customized fatty acid profiles. This review explores the capabilities of key enzymes involved in fatty acid and triacylglycerol synthesis, including fatty acid synthases, desaturases, elongases, and acyltransferases. It discusses factors influencing fatty acid composition and presents engineering strategies to enhance fatty acid synthesis. Specifically, we highlight successful engineering approaches to modify fatty acid profiles in triacylglycerols and produce tailored fatty acids, and we offer recommendations for host selection to streamline engineering efforts.</p> Key points <p>• <i>Detailed overview on all basic aspects of fatty acid metabolism in yeast</i></p> <p>• <i>Comprehensive description of fatty acid profile tailoring in yeast</i></p> <p>• <i>Extensive summary of applying tailored fatty acid profiles in production processes</i></p> Graphical abstract <p></p>