<p>Terraforming Mars has long captured the imagination but has received surprisingly little rigorous study. Progress in Mars science, climate science, launch capabilities and bioscience motivates a fresh look at Mars terraforming research. Since Sagan’s time, it has been understood that terraforming Mars would involve warming to enable oxygenic photosynthesis by engineered microbes, followed by slow oxygen build-up enabling more complex life. Before we can assess whether warming Mars is worthwhile, relative to the alternative of leaving Mars as a pristine wilderness, we must confront the practical requirements, cost and possible risks. Here we discuss what we know about Mars’s volatile inventories and soil composition, and possible approaches to warm Mars and increase atmospheric O₂. New techniques have emerged that could raise Mars’s average global temperature by tens of degrees within a few decades. Research priorities include focusing on understanding fundamental physical, chemical and biological constraints that will shape any future decisions about Mars. Such research would drive advances in Mars exploration, bioscience and climate modelling.</p>