To meet the demands of future generations for chemicals and energy and to reduce the environmental footprint of the chemical industry, alternatives for petrochemistry are required. Microbial conversion of renewable feedstocks has a huge potential for cleaner, sustainable industrial production of fuels and chemicals. Microbial production of organic acids is a promising approach for production of chemical building blocks that can replace their petrochemically derived equivalents. Although Saccharomyces cerevisiae does not naturally produce organic acids in large quantities, its robustness, pH tolerance, simple nutrient requirements and long history as an industrial workhorse make it an excellent candidate biocatalyst for such processes. Genetic engineering, along with evolution and selection, has been successfully used to divert carbon from ethanol, the natural endproduct of S. cerevisiae, to pyruvate. Further engineering, which included expression of heterologous enzymes and transporters, yielded strains capable of producing lactate and malate from pyruvate. Besides these metabolic engineering strategies, this review discusses the impact of transport and energetics as well as the tolerance towards these organic acids. In addition to recent progress in engineering S. cerevisiae for organic acid production, the key limitations and challenges are discussed in the context of sustainable industrial production of organic acids from renewable feedstocks.