The extinct warrah is sometimes taken as evidence of pre-European discovery.
The islands were uninhabited when they were first discovered by European explorers. There is disputed evidence of prior settlement such as the presence of the Falkland Island fox, or Warrah (now extinct). Humans may have brought them to the islands, but they may have reached the islands via a land bridge when the sea level was much lower during the last ice age. There is also a scattering of undated artifacts including arrowheads and the remains of a canoe.

The first European explorer to sight the islands is widely thought to be Sebald de Weert, a Dutch sailor, in 1600. Although several British and Spanish historians maintain their own explorers discovered the islands earlier, some older maps, particularly Dutch ones, used the name "Sebald Islands", after de Weert.

In January 1690, English sailor John Strong, captain of the Welfare, was heading for Puerto Deseado (now in Argentina); but driven off course by contrary winds, he reached the Sebald Islands instead and landed at Bold Cove. He sailed between the two principal islands and called the passage "Falkland Channel" (now Falkland Sound), after Anthony Cary, 5th Viscount Falkland, who as Commissioner of the Admiralty had financed the expedition (Cary later became First Lord of the Admiralty). The island group later took its English name from this body of water.

Since their discovery, the Falkland Islands have had a complex history. France, Britain, Spain, and Argentina have all claimed possession at some time, and have established and abandoned settlements on the islands. The Falklands Crisis of 1770 was nearly the cause of a war between a Franco-Spanish Alliance and Britain. Argentina took over and continued the Spanish government's claim after its declaration of independence in 1816 and the independence war in 1817. The American sloop USS Lexington destroyed the Argentine settlement at Puerto Luis on 28 December 1831 and the United Kingdom returned to the islands in 1833. Argentina has continued to claim sovereignty over the islands, and the dispute was used by the military junta as a pretext to invade and briefly occupy the islands before being defeated in the two-month-long Falklands War in 1982, by a United Kingdom task force which returned the islands to British control.

The first settlement on the Falkland Islands was in 1764. It was called Port St. Louis and was founded by the French navigator and military commander Louis Antoine de Bougainville on Berkeley Sound, in present-day Port Louis, East Falkland.

In January 1765, the British captain John Byron, unaware of the French presence, explored and claimed Saunders Island, at the western end of the group, where he named the harbour of Port Egmont. He sailed near other islands, which he also claimed for King George III. A British settlement was built at Port Egmont in 1766. Also in 1766, Spain acquired the French colony, and after assuming effective control in 1767, placed the islands under a governor subordinate to the Buenos Aires colonial administration. Spain attacked Port Egmont, ending the British presence there in 1770. The expulsion of the British settlement brought the two countries to the brink of war, but a peace treaty allowed the British to return to Port Egmont in 1771 with neither side relinquishing sovereignty.

As a result of economic pressures resulting from the forthcoming American Revolutionary War, the United Kingdom decided to withdraw unilaterally from many of her overseas settlements, including Port Egmont, in 1774. Upon her withdrawal in 1776 the UK left behind a plaque asserting her claims. From 1776 until 1811 Spain maintained a settlement administered from Buenos Aires as part of the Viceroyalty of the Rio de la Plata. On leaving in 1811, Spain also left behind a plaque asserting her claims.

On 6 November 1820, Colonel David Jewett raised the flag of the United Provinces of the River Plate (Argentina) at Port Louis. Jewett was an American sailor and privateer in the employment of Buenos Aires businessman Patrick Lynch to captain his ship, the frigate Heroína (Lynch had obtained a corsair licence from the Buenos Aires Supreme Director Jose Rondeau). Jewett had put into the islands the previous month, following a disastrous eight month voyage with most of his crew disabled by scurvy and disease. After resting in the islands and repairing his ship he returned to Buenos Aires.

Occupation began in 1828 with the foundation of a settlement and a penal colony. United States warships destroyed this settlement in 1831 after the Argentine governor of the islands Luis Vernet seized US seal hunting ships during a dispute over fishing rights. Escaped prisoners and pirates were left behind. In November 1832, Argentina sent another governor who was killed in a mutiny.

In January 1833, British forces returned and informed the Argentine commander that they intended to reassert British sovereignty. The existing settlers were allowed to remain, with an Irish member of Vernet's settlement, William Dickson, appointed as the Islands' governor. Vernet's deputy, Matthew Brisbane, returned later that year and was informed that the British had no objections to the continuation of Vernet's business ventures provided there was no interference with British control.

The Royal Navy built a base at Stanley, and the islands became a strategic point for navigation around Cape Horn. A World War I naval battle, the Battle of Falkland Islands, took place in December 1914, with a British victory over the Germans. During World War II, Stanley served as a Royal Navy station and serviced ships which took part in the Battle of the River Plate.

Sovereignty over the islands again became an issue in the latter half of the 20th century. Argentina, in the pursuit of its claim to the islands, saw the creation of the United Nations as an opportunity to present its case before the rest of the world. In 1945, upon signing the UN Charter, Argentina stated that it reserved its right to sovereignty of the islands, as well as its right to recover them. The United Kingdom responded in turn by stating that, as an essential precondition for the fulfilment of UN Resolution 1514 (XV) regarding the de-colonisation of all territories still under foreign occupation, the Falklanders first had to vote for the British withdrawal at a referendum to be held on the issue.

Talks between British and Argentine foreign missions took place in the 1960s, but failed to come to any meaningful conclusion. A major sticking point in all the negotiations was that the two thousand inhabitants of mainly British descent preferred that the islands remain British territory.