Tolkien: Genealogy of Aragorn and Arwen
The Half-elven were those that descended from both Elves and Men. At the end of the First Age of the Sun, the Half-elven were given an irrevocable choice as to which kindred they wished to be judged. Eärendil and Elwing chose to be counted among Elves. Their sons, Elros and Elrond, were also given a choice. Elros chose to be counted among Men. Elrond chose to be counted among Elves. Aragorn and Arwen can trace their lineage to the Maiar, the three races of the Eldar (Vanyar, Noldor, and Teleri), the Sindar, and the three houses of the Edain (Bëor, Haladin, and Marach).