The potential loss or large-scale degradation of the tropical rainforests has become one of the iconic images of the impacts of twenty-first century environmental change and may be one of our century's most profound legacies. In the Amazon region, the direct threat of deforestation and degradation is now strongly intertwined with an indirect challenge we are just beginning to understand: the possibility of substantial regional drought driven by global climate change. The Amazon region hosts more than half of the world's remaining tropical forests, and some parts have among the greatest concentrations of biodiversity found anywhere on Earth. Overall, the region is estimated to host about a quarter of all global biodiversity. It acts as one of the major 'flywheels' of global climate, transpiring water and generating clouds, affecting atmospheric circulation across continents and hemispheres, and storing substantial reserves of biomass and soil carbon. Hence, the ongoing degradation of Amazonia is a threat to local climate stability and a contributor to the global atmospheric climate change crisis. Conversely, the stabilization of Amazonian deforestation and degradation would be an opportunity for local adaptation to climate change, as well as a potential global contributor towards mitigation of climate change. However, addressing deforestation in the Amazon raises substantial challenges in policy, governance, sustainability and economic science. This paper introduces a theme issue dedicated to a multidisciplinary analysis of these challenges.