The Lords of Andúnië, named for the haven of Andúnië where they lived, were descended from Silmariën, daughter of Tar-Elendil the fourth King of Númenor. She would have been the Ruling Queen according to later laws.
They remained faithful to the Valar and remained Elf-friends even after Númenor had fallen into darkness, and were held as leaders of the Faithful (as opposed to the King's Men).
At the end of the Second Age, the Lord of Andúnië was Amandil the Faithful, who for years was a friend of Ar-Pharazôn the King, until Sauron dismissed him. He sailed into the west to seek pardon of the Valar for the wickedness of the Númenóreans, but was never heard of again.
His son Elendil, the last Lord of Andúnië, did not join the fleet of Ar-Pharazôn to attack Valinor, and fled with his sons Isildur and Anárion and many of the Faithful to Middle-earth, where they founded the lines of the Kings of Gondor and Arnor.