In his epic Lord of the Rings Trilogy, J. R. R. Tolkien singlehandedly redefined the popular concept of elves, changing them from the diminutive woodland sprites of folklore, to the noble, ancient race which has appeared in countless fantasy millieus since. However, LotR was just a story that had elves in it. For the true history of elves, we turn to the Silmarillion, Tolkien's posthumously published tale of the origins of the races of Elves and Men.

The Quendi

It is told that even as Varda ended her labours, and they were long, when first Menelmacar strode up the sky and the blue fire of Helluin flickered in the mists above the borders of the world, in that hour the Children of the Earth awoke, the Firstborn of Ilúvatar. [Silmarillion, p. 48]

The Quendi, or "those that speak with voices", were the eldest of the humanoid races in Tolkien's world. When Oromë discovered them, he called them the Eldar, "the people of the stars", though that name later came to apply only to those who at least began the Great Journey to Aman. Those who did not became known as the Avari, "the Unwilling".

The Eldar

Of those who heeded the summons of the Valar, there were three hosts that ventured forth. The Vanyar, the Noldor, and the Teleri.

The Vanyar

Led by Ingwë, the first host of the Eldar passed swiftly into the west, and never again concerned themselves with Middle Earth. They are among those known as the Calaquendi, those elves who saw the Aman in the light of the Two Trees.

The Noldor

Led by Finwë, they came next into Aman. However, following the theft of the Silmarils, many of them followed the Sons of Fëanor back to Middle Earth to wage war apon Morgoth. They too are numbered among the Calaquendi.

The Teleri

The third and last host host to leave the ancestral home of the elves, the Teleri were led by Elwë Singollo, later called Elu Thingol in the Sindarin tounge, and his brother Olwë. Along the westward march, the Teleri splintered, as one known as Lenwë led a faction southward along the river Anduin. These were known as the Nandor, and are counted among the Moriquendi, the elves who never saw the light of the Trees. Many years later, some of the Nandor, led by Denethor, Lenwë's son, eventually traveled west, and became known as the Laiquendi.

The remainder of the Teleri eventually followed the Vanyar and the Noldor over the Misty Mountains. However, as they neared the sea, the Teleri rested in East Beleriand. As they camped there, Elwë made his way west, to seek out his friend Finwë, who lead the Noldor. Thus he came to the wood of Nan Elmoth, and there he heard the singing of the Maia Melian. So great was the beauty of her voice, that Elwë sought her out.

...[H]e came at last to a glade, open to the stars, and there Melian stood; and out of the darkness he looked at her, and the light of Aman was in her face.

She spoke no word, but being filled with love Elwë came to her and took her hand, and straightaway a spell was laid on him, and so that they stood thus while long years were measured by the wheeling stars above them....
[Silmarillion, p. 58]

The Teleri searched for their king in vain, and eventually Olwë took the kingship, and led half of the remaining Teleri across the sea to Aman, where they became the third group of Calaquendi.

Those Teleri that remained in Beleriand, became known as the Sindar, the grey elves, and Elwë returned to them as their king, with Melian as his queen. The Sindar and the Nandor/Laiquendi are known as the Úmanyar, the elves "not of Aman, and are also counted among the Moriquendi.


                         Quendi
                            |
                 +----------+----------------------+
                 |                                 |
               Eldar                              Avari
                 |
   +---------+---+----------+
   |         |              |
 Vanyar    Noldor         Teleri
                            |
                     +------+----+--------+
                     |           |        |  
                (Those that   Sindar   Nandor
                  went to                 |
                  Aman)               Laiquendi
                              \                  /
  \                         /  \----------------/
   \-----------------------/          |
           |                       Úmanyar
           |
           |                    \                         /
           |                     \-----------------------/
           |                                   |
      Calaquendi                        Moriquendi
Chart is from the Silmarillion, page 383, ASCII-ized by yours truly.
Page Numbers are from the Ballantine paperback edition. YMMV.