Natural products are a group of bioactive structurally diverse chemicals produced by microorganisms and plants. These molecules and their derivatives have contributed to over a third of the therapeutic drugs produced in the last century. However, over the last few decades traditional drug discovery pipelines from natural products have become far less productive and far more expensive. One recent development with promise to combat this trend is the application of synthetic biology to therapeutic natural product biosynthesis. Synthetic biology is a young discipline with roots in systems biology, genetic engineering, and metabolic engineering. In this review, we discuss the use of synthetic biology to engineer improved yields of existing therapeutic natural products. We further describe the use of synthetic biology to combine and express natural product biosynthetic genes in unprecedented ways, and how this holds promise for opening up completely new avenues for drug discovery and production.