The earliest claim was sketched not by either rival but by the Vatican. In 1493, a year after Columbus, Pope Alexander VI divided the unexplored New World between Spain and Portugal, and the Treaty of Tordesillas the following year fixed the line. The Falklands fell on the Spanish side. Yet no European is known to have set foot on them until 1690, when the Englishman John Strong sailed through the channel he named Falkland Sound. The first actual settlers were French: in 1764 the explorer Louis Antoine de Bougainville founded Port-Saint-Louis on East Falkland with some 250 colonists. The British arrived almost simultaneously, planting a fort called Port Egmont in 1766, often without realising another European power was already on the far side of the islands.

Ownership then passed hand to hand in a tangle that both sides still mine for arguments. Spain bought out the French, very nearly went to war with Britain in 1770, and eventually held the islands as the British quietly withdrew in 1774, leaving behind a plaque to mark that they had not surrendered their claim. When Spain's American empire collapsed, the newly independent United Provinces, the seed of modern Argentina, asserted that the Falklands had passed to them by inheritance. They established a settlement under Louis Vernet, whose own daughter was born on the islands and named Malvina. Then in 1831 an American warship, the USS Lexington, raided Vernet's colony over a dispute about seal hunting and left it in ruins, its captain declaring the place to belong to no one at all.

The modern dispute crystallised in January 1833, when a British squadron arrived and asked the small Argentine garrison to lower its flag and leave. Argentina calls this an act of force, an illegal seizure it has protested ever since, in 1841, 1849, and on through more than a dozen formal objections to the present day. Britain replies that no settled population was expelled, only a garrison, and that the islands had no indigenous people and only the most fleeting prior occupation. Argentina counters that the islanders are a transplanted British population with no separate right of self-determination. Britain holds that self-determination is a universal right and the islanders' wishes are decisive. Both cases are sincerely argued and genuinely complicated, and reasonable people in both countries believe their own with complete conviction.

By 1982 Argentina was governed by a military junta presiding over economic ruin and rising public anger, and recovering the Malvinas promised a unifying triumph. On 2 April its forces invaded. The 74-day war that followed killed 649 Argentines, 255 British servicemen, and three islanders before Argentine forces surrendered at Stanley on 14 June. The quarrel did not end with the fighting. Argentina still claims the islands in its constitution and raises the issue yearly at the United Nations. The islanders, for their part, answered in their own voice in March 2013, when a referendum asked whether they wished to remain a British Overseas Territory. Of 1,516 valid votes, all but three said yes, on a turnout of more than ninety percent. Argentina dismissed the vote; Britain called it decisive. The two names endure, and so does the argument between them.