Organic acids are organic compounds that can be synthesized using biological systems. They often contain one or more low molecular weight acidic groups, such as carboxyl group and sulphonic group. Organic acids are widely used in food, agriculture, medicine, bio-based materials industry and other fields. Yeast has unique advantages of biosafety, strong stress resistance, wide substrate spectrum, convenient genetic transformation, and mature large-scale culture technology. Therefore, it is appealing to produce organic acids by yeast. However, challenges such as low concentration, many by-products and low fermentation efficiency still exist. With the development of yeast metabolic engineering and synthetic biology technology, rapid progress has been made in this field recently. Here we summarize the progress of biosynthesis of 11 organic acids by yeast. These organic acids include bulk carboxylic acids and high-value organic acids that can be produced naturally or heterologously. Finally, future prospects in this field were proposed.