Greenland is somewhere between an island and a continent, and also somewhere between a country and a territory of Denmark. Why haven't these issues ever been resolved? Because there aren't enough people in Greenland to worry about it. With about the same land area as Mexico and enough people to almost fill one football stadium, Greenland has the lowest population density in the world.
Part of the biggest real-estate scam in history, the popular tale goes that Greenland's name was traded with Iceland so that colonizing populations would mistake it for the temperate, beautiful destination that is Iceland today.
What to do
Visit the summit, the highest point on Greenland and one of the most studied and drilled places on the island. Also stay in a fishing village and see what may be the last practitioners of a dying profession.
The Danish government, which still technically holds sway over Greenland, allows it to self-govern and provide its citizens with welfare, unemployment and retirement benefits that rival any major nation. Denmark continues to support Greenland, even though it must pay subsidies in order to keep the population afloat economically. Greenland's main natural revenue source is fish and in recent years catches haven't been good enough for the fisheries to turn a profit.
The world's eye has warily turned to Greenland recently as global climate change threatens to melt the vast ice shelves sitting on the top of Greenland and send our ocean levels skyrocketing. Who knows, maybe Greenland will become a welcoming travel destination in the next few decades.
Flights to Greenland generally come in to the Kangerlussuaq or Narsarsuaq airport. From there you'll have to catch a boat or ferry to your final destination.
Where to stay
Greenland's hotels stick to the cities, but spending the night in one of them is expensive. Greenland doesn't see many travelers, so running a hotel is an expensive proposition. The closest thing you're going to find to a hostel is a room in a local's house, which can be booked through the Nuuk (that's a city) tourism office.