House of Elendil
Elendil the son of Amandil with his two sons Isildur and Anárion, he escaped the Downfall of Númenor and founded two kingdoms in Middle-earth; Arnor in the north, and Gondor in the south. He ruled both of these as High King of the Dúnedain, and from his descendants came the line of Kings in both the North- and the South-kingdoms.
Elendil himself was lost in the Siege of Barad-dûr, and his elder son Isildur inherited the High Kingship. Two years later, Isildur himself, together with his three elder heirs, was lost in the Disaster of the Gladden Fields. His only remaining heir, Valandil, was only a boy, and so Arnor was effectively left without a King. Thus, the House of Elendil split into two lines. In the south, Isildur's nephew Meneldil had been left to rule Gondor in his uncle's name. Meneldil now took up the full Kingship of Gondor, and it was ruled by his descendants for more than two thousand years.
When Valandil came of age, he inherited the northern lands of his father, Arnor. Valandil and his descendants ruled the North-kingdom for many generations, until dissent arose among the sons of the tenth King, Eärendur. This conflict ultimately saw Arnor divided into three kingdoms; Arthedain, Cardolan and Rhudaur. Eärendur's eldest son and true heir, Amlaith, took control of Arthedain, while his brothers took up rule in the other new lands. Arthedain endured for more than a thousand years, but eventually all three kingdoms of the Northern Dúnedain fell to the armies of Angmar.
The line of Elendil was not broken in that defeat. The heir of Arvedui, the last King of Arthedain, was Aranarth. He took the title Chieftain of the Dúnedain, and his descendants led a proud but scattered people through the last millennium of the Third Age. The last Chieftain was Aranarth's heir through many generations: Aragorn II, who united the Two Kingdoms after the War of the Ring and became the first King of the Reunited Kingdom, thus the House of Elendil returned to Gondor.