According to the Central Intelligence Agency's World Factbook, Greenland is 2.2 million square kilometres, with 1.7 million of that covered in ice. It has considerable natural resources, such as coal and uranium, but only 0.6 percent of the land is used for agriculture. It has around 58,000 residents, making it one of the world's smallest countries by population.
It is a self-governing country that is part of the kingdom of Denmark. Trump is scheduled to visit Denmark in two weeks.
Trump has touted his career as a real estate developer during the 2016 presidential campaign and made clear that he has retained an eye for real estate opportunities during his tenure in the White House. For example, he has said that North Korea could build famous hotels and resorts along its oceanfront properties, even though many foreigners are afraid to visit the country out of fear for their lives.
Typically, Congress must appropriate money before the White House can use it, but Trump has already shown a willingness to get around those restrictions.
Some on Thursday night responded to the news with incredulity; others, with support.
"This idea isn't as crazy as the headline makes it seem," Rep. Mike Gallagher, R-Wis., said in a tweet. "This a smart geopolitical move. The United States has a compelling strategic interest in Greenland, and this should absolutely be on the table."
Most, however, responded with mockery.
Rep. Steve Cohen, D-Tenn., shared a news story about Trump's idea and mused: "A Great place for his 'presidential' library."
And Jonah Goldberg, a fellow at the American Enterprise Institute, tweeted that MAGA - the acronym for Trump's "Make America Great Again" campaign slogan - is "an an anagram of Make Greenland American Already."
