Half-Elves were the child of a mortal and an immortal parent. While the term Half-Elf or Peredhel proper only refers to the family of Earendil and Elwing, the only acknowledged union between Eldar and Edain, there certainly were more and less known unions between Dark Elves and Hildor; for example - Galador of Dol Amroth and Erestor of Imladris.
At one point of his life a Half-Elf had to choose, intentionally or unconsciously, if he wanted to live the eternal life of the Quendi or the mortal life of the Hildor, this responsibility could also be inherited by the children and grand-children of a half-elf if they were born before he had made his choice.
The descendants of Half-Elves were, even if the Half-elven parent chose a mortal life, regarded as Elf-blooded and often inherited a long lifespan and exceptional beauty and aura as well as other strengths of the Quendi.
Half-Elves and Elf-blooded of Renown
Andai Inda'eir Annelena Ardagor Arwen Undómiel Blodrin Bolg the Younger Carambor Chinta Kari Darien Dior Aranel Eärendil the Mariner Eldarion Telcontar Elladan Elor once Dark Elrohir Elrond Half-elven Elros Tar-Minyatur Eluréd Elurín Elwing Erestor of Rivendell Galador of Dol Amroth Gilmith of Dol Amroth El'ugni Heorrenda Jaeru Jax Kôma of Kôm Lúthien Tinúviel Marahil Mirag Moran Morelen Namu the Rain-man Ingi'inda Grey-cloaked Sérëdhiel Shaleen T'revor Arain Tiliwini Tinfang Gelion Ulgarin Yark Balka