One of the bright stars placed in the sky by Varda at the time of the awakening of the Elves in Middle-earth. Its identity is uncertain, though the fact that its name contains the Elvish word luin, meaning 'blue', does offer a clue.
The only remote explanation offered by Tolkien was a rough and uncertain note that seems to link Luinil to the planet we call Neptune. As Christopher Tolkien notes, though, this dark and distant object, too faint to be seen by the naked eye, would hardly qualify as a 'bright star'. Another alternative would be blue Rigel in Orion, making Luinil the mate of red Borgil. Two other possibilities - based purely on the fact that they are both bright blue stars - would be Spica in Virgo or Regulus in Leo.