France, Spain, the UK, and Argentina have tussled over ownership of the Falkland Islands since the 16th century. France and Spain gave up long ago, leaving the UK in possession and Argentina claiming sovereignty.
Argentina occupied the islands in 1982, leading to a month-long losing war with the UK. Since the war, British military spending has become a major part of the Falkland Islands economy, along with farming and fishing.
As of 2012 the population was less than 3,000 people. Many areas of the island are still filled with land mines and ordnance from the Falkland War. If you visit, be sure to pick up a free map from the EOD (Explosive Ordnance Disposal) office in Stanley, West Falkland, detailing where not to step.
Falkland Islands on Wikipedia