Arwen was the youngest child of Elrond and Celebrían; her elder brothers were the twins Elladan and Elrohir.
As told in "The Tale of Aragorn and Arwen", found in Appendix A to The Lord of the Rings (after the third volume, The Return of the King), during Aragorn's twentieth year he met Arwen for the first time in Rivendell, where he lived under Elrond's protection. Arwen, then over 2700 years old, had recently returned to her father's home after living for a while with her grandmother Galadriel in Lórien. Aragorn fell in love with Arwen at first sight. About thirty years later, the two were reunited in Lórien; at that time, Arwen reciprocated Aragorn's love; then they "plighted their troth" (promised themselves to each other) on the mound of Cerin Amroth.
Arwen's first appearance in The Lord of the Rings proper was at Rivendell, when the Hobbits arrived there, and Aragorn was seen with her — the first hint of their relationship. Later, when the Fellowship of the Ring came to Lothlórien, Aragorn remembered their earlier meeting and paused in reverence on Cerin Amroth.
Arwen was a very distant relative of her husband Aragorn. Aragorn's ancestor, Elros Tar-Minyatur, the first King of Númenor, was her father Elrond's brother, who chose to live as a Man rather than one of the Eldar. Arwen eventually became Queen of the Reunited Kingdom of Arnor and Gondor when she married Aragorn, who was of the line of the Kings of Arnor. By Arwen and Aragorn's marriage, the long-sundered lines of the Half-elven were joined. Their union also served to unite and preserve the bloodlines of the Three Kings of the High Elves (Ingwë, Finwë, and the brothers Olwë and Elwë) as well as the only line with Maiarin blood through Arwen's great-great-great grandmother, Melian, Queen of Doriath, and also on Aragorn's side, through the line of kings of Arnor and Númenor to Elros, Elrond's brother, whose great-great-grandmother was also Melian.