The lands of Eldar in the Undying Lands were called Eldamar, meaning 'elvenhome' in Elvish.

Here the greatest of the Elves from among the three kindred of the Vanyar, Noldor and Teleri people lived with the mighty Valar.

Eldamar was that part of the Undying Lands east of Valinor and west of the Great Sea. It was founded in the Second Age of the Two Trees of Valinor when the first Eldar arrived in the Undying Lands.

The cities of Eldamar were wealthy and beautiful beyond comparison. The main city was Tirion. Its crops of grain and fruits were bountiful and its people happy, resourceful and wise.

After the disaster of NĂºmenor and the Change of the World at the end of the Second Age of the Sun, Eldamar, along with the rest of the Undying Lands, was taken out of the circles of the world, and beyond the understanding of mortals.
Encyclopedia entry originally written by whats_taters_eh?