When it leaked out in August 2019 that US president Donald Trump was considering the possibility of purchasing Greenland, reactions ranged between indignation and irony. But US renewed attention towards this Arctic land reflects the growing interest in the polar regions, largely because of their natural resources. Might it be possible today for a country, whichever it might be, to purchase a territory like Greenland that has a large degree of autonomy within the kingdom of Denmark but is also thereby associated with the European Union? What is its status? What are its sources of finance and its assets? What interests are in play? Jean-François Drevet casts an eye over the subject, showing the different issues in play for a territory coveted by its near neighbours and also by China.