Malaria is a life-threatening disease. Artemisinin-based combination therapy (ACT) is the preferred choice for malaria treatment recommended by the World Health Organization. At present, the main source of artemisinin is extracted from Artemisia annua; however, the artemisinin content in A. annua is only 0.1–1%, which cannot meet global demand. Meanwhile, the chemical synthesis of artemisinin has disadvantages such as complicated steps, high cost and low yield. Therefore, the application of the synthetic biology approach to produce artemisinin in vivo has magnificent prospects. In this review, the biosynthesis pathway of artemisinin was summarized. Then we discussed the advances in the heterologous biosynthesis of artemisinin using microorganisms (Escherichia coli and Saccharomyces cerevisiae) as chassis cells. With yeast as the cell factory, the production of artemisinin was transferred from plant to yeast. Through the optimization of the fermentation process, the yield of artemisinic acid reached 25 g/L, thereby producing the semi-synthesis of artemisinin. Moreover, we reviewed the genetic engineering in A. annua to improve the artemisinin content, which included overexpressing artemisinin biosynthesis pathway genes, blocking key genes in competitive pathways, and regulating the expression of transcription factors related to artemisinin biosynthesis. Finally, the research progress of artemisinin production in other plants (Nicotiana, Physcomitrella, etc.) was discussed. The current advances in artemisinin biosynthesis may help lay the foundation for the remarkable up-regulation of artemisinin production in A. annua through gene editing or molecular design breeding in the future.