Climate change has revived debates around the concept of limits to growth, 45 years after it was first proposed. Many citizens, scientists and politicians fear that stringent climate policy will harm economic growth. Some are anti-growth, whereas others believe green growth is compatible with a transition to a low-carbon economy. As the window to curb warming at 2 °C closes, this debate will intensify. This Review critically reflects on both positions, providing an overview of existing literature on the growth versus climate debate. Both positions are argued here to jeopardize environmental or social goals. A third position, labelled an 'agrowth' strategy, is proposed to depolarize the debate and reduce resistance to climate policies.