In J.R.R. Tolkien's Middle-earth, the High Kings of Arnor and Gondor were the Kings of all Dúnedain in Middle-earth after the Downfall of Númenor. Elendil was the leader of the Elendili who survived the Downfall. He claimed the title of High King.
There were only two High-Kings of Arnor and Gondor before the sundering of the two Kingdoms. Those kings were Elendil the Tall and his son Isildur. After the death of Isildur in T.A. 2, his son Valandil succeeded him as King of Arnor, while his brother Anárion's son Meneldil succeeded him as King of Gondor. Valandil never attempted to assert power over Gondor, and thus Isildur is counted as the last High King of both Realms, but the descendents of Valandil continued to use the title High King of Arnor. Later, after the death of Ondoher of Gondor, Arvedui of Arthedain claimed the Kingship over Gondor as the rightful heir of Isildur, but the Council of Gondor, influenced by Steward Pelendur refused Arvedui's claim, saying that Isildur forsook the Kingdom to Meneldil, and that only the heirs of Anárion could be King of Gondor.
Arvedui would become the last King of Arnor, and his descendants, the Chieftains of the Dúnedain never attempted to claim the throne of Gondor, nor the High Kingship. Only at the beginning of the Fourth Age, the two kingdoms came under one ruler again as the Reunited Kingdom (see Kings of the Reunited Kingdom) under Elessar Telcontar.