Peredhil

Eärendil was the son of an Elf (Idril) and a Man (Tuor), and thus had a claim to belong to either race. When he reached Valinor, the Valar gave him a choice: whether to be counted among Elves or Men. It is said that he thought of himself rather as a Man than an Elf, but for the sake of his wife Elwing he chose the immortality of the Elves.

The same choice descended to Eärendil's sons Elrond and Elros, and thus they gained the title Peredhil, 'Half-elven'. Elrond chose to be counted among the Elves, Elros among Men. Again the choice passed down to Elrond's children, so that Arwen was able to abandon her immortality to become queen to Aragorn. (Elros' descendants did not have the choice; they remained mortal, kings of the royal line of Númenor).