Acrylic acid (AA) is a chemical with high market value used in industry to produce diapers, paints, adhesives and coatings, among others. AA available worldwide is chemically produced mostly from petroleum derivatives. Due to its economic relevance, there is presently a need for innovative and sustainable ways to synthesize AA. In the past decade, several semi-biological methods have been developed and consist in the bio-based synthesis of 3-hydroxypropionic acid (3-HP) and its chemical conversion to AA. However, more recently, engineered Escherichia coli was demonstrated to be able to convert glucose or glycerol to AA. Several pathways have been developed that use as precursors glycerol, malonyl-CoA or β-alanine. Some of these pathways produce 3-HP as an intermediate. Nevertheless, the heterologous production of AA is still in its early stages compared, for example, to 3-HP production. So far, only up to 237 mg/L of AA have been produced from glucose using β-alanine as a precursor in fed-batch fermentation. In this review, the advances in the production of AA by engineered microbes, as well as the hurdles hindering high-level production, are discussed. In addition, synthetic biology and metabolic engineering approaches to improving the production of AA in industrial settings are presented.