As related by J.R.R. Tolkien, the third and final (and largest) kindred of the Eldar to follow Oromë from Cuiviénen to the relative safety of Aman and the light of the Two Trees, led by the brothers Elwë and Olwë.
The Teleri were not as willing to travel as the Noldor and Vanyar, and during their journey across Middle-Earth, they became fragmented. One group, led by Lenwë, broke off and wandered on their own. These were the Nandor, who eventually wandered into Beleriand and became the Green-Elves of Ossiriand.
While waiting for Ossë to drag Tol Eressëa back across the great sea Belegaer to pick them up, the rest of the Teleri settled on the western shores of Beleriand, becoming shipwrights and mariners.
Meanwhile, Elwë had wandered off into the forest of Doriath and fallen in love with the Maia Melian. Many of Elwë's kinsmen began to search for him. When Oromë and Ossë returned, most of the Teleri followed Olwë and finished their journey to Aman, and some stayed behind in their havens (led by Círdan), or in Doriath with Elwë (aka Thingol), becoming one of the components of the Sindar.
Driven by of their love of the sea, those Teleri who continued on to Aman persuaded Ossë to fix Tol Eressëa in the Bay of Eldamar. The Valar opened a pass in the Pelóri (called Calacirya) in order for the light of the Two Trees to shine into Eldamar.
The most infamous event in Eldamar was the Kinslaying of Alqualondë, when the most of the Noldor, led by Fëanor, slaughtered many Teleri (including Olwë) in order to steal their ships to carry them back to Middle-Earth.
During the Second Age, the Teleri would trade with Númenor. Since the Dúnedain were forbidden to sail west to Aman, this always happened in Númenor's western port of Andunië. The Palantiri were the most famous items acquired via this trade. When the Númenoreans became corrupt and arrogant, the Teleri ceased sailing there, and even abandoned Tol Eressëa.