Because of its isolation, it took almost two centuries to the Europeans to discover Tahiti and her islands. And today, it is still obviously the same relative isolation  that protects them as a haven of peace and serenity.

Although navigators had been criss-crossing the area: In 1521, Magellan stopped on the atoll of Puka Puka in the Tuamotus. It is only in 1595 that Alvaro de Mendana, coming from Spanish possessions in Latin America, discovered the Marquesas. In 1606, Fernando de Quiros sailed through the Tuamotu as well as Dutchmen Le Maire and Schouten in 1616,  and a century later in 1722, Roggeven, who after discovering Easter Island, sailed through the Tuamotus and  discovered Maupiti much more to  the West.

But it was in June 1767 that Samuel Wallis, sailing further South, finally discovered the island of Tahiti, followed ten months later by French explorer Louis-Antoine de Bougainville and on April 13 1769 by James Cook on his famous 3-mast ship "The Endeavour".. Site of the Endeavour's replica 

Bougainville brought enthousiastic storie from his trip and the two weeks he spent in Tahiti and contibuted widely to creating the myth of a Polynesian paradise, completed by the observations of astronomer Véron and naturalist Commerson, who participated in the expedition aboard the 2 ships " La Boudeuse " and " L'Etoile". 

But it was truly the expedition lead by James Cook on "The Endeavour"  in 1769 that brought back quantities of geographical and anthropological information on the Society Islands, with very accurate topographic measurements and the presence, during his two other  expeditions in Tahiti in 1773 and in 1779, of botanists, painters and astronomers. 

In 1789, William Bligh, after the famous Bounty mutiny, drifted on a long boat all the way to the Dutch Indies, while a group of mutineers lead by Fletcher Christian found shelter on the island of Pitcairn located East of the Austral Islands, and  another group played a major role in Tahiti's inter-tribal conflicts before being brought back by the British Navy.  

And also...

The first Maohi settlements...

British ships at the time used to anchor on the North side of Tahiti at Venus Point. Around 1790, the local chief allied himself with the Bounty mutineers who came back to settle in  Tahiti and he imposed a monarchic power under the name Pomare. His son, who took the name Pomare II in 1803, was the first to convert and to learn to read and write. In 1815, he won the battle of Fe'i Pi against traditionalist clans. This battle settled the political fate of the archipelago and he was proclaimed to the supreme rank of ari'i rahi (King of Kings) of Tahiti. Following the death of his young brother Pomare III, Queen Pomare IV came to power, reigned for 50 years and was forced to accept France's protectorate in 1842. From 1844 to 1846, many battles opposed the French and chiefs hostile to   French presence.  In 1881, her son, King Pomare V accepted to change his Kingdom into a colony of the French State.