This report reviews recent thinking and debates about physical limits to human activities, and particularly the concept of ‘planetary boundaries’. It looks at the scientific basis of the planetary boundaries concept and its claims for novelty, and the most recent update of the original proposition and analysis. I suggest that geographers can invigorate and inform the science of planetary boundaries by further developing conceptualizations of human-environment relations; by constructing a political ecology of planetary boundaries; by exploring alternative development pathways; and by dissecting the planetary and its relations across scales. These present crucial challenges, necessitating joined-up, dynamic and novel approaches.