[Finwe]

The full story is in the Appendices to Return of the King, but I'll try to explain it as best I can.

As you know, with the original founding of Arnor and Gondor, the two lines of Elendil were split. Anarion's line ruled the South, and Isildur's line was supposed to rule the North, except, he (so very intelligently) managed to get himself killed along with his three eldest sons at the Gladden Fields. Thankfully, his youngest son, Valandil, was in Rivendell, so when he got old enough, he took up the throne. That went on, until the time of King Earendur, who had three sons. That was when Arnor got divided up into Arthedain, Rhudaur, and Cardolan.

For a while, things were nice and rosy. But the bloodlines of Rhudaur and Cardolan became intermingled with those of lesser Men, so after a while, it was only the line of Arthedain that had "true" Numenorean blood. The others got jealous, and along with the help of the Witch-king, drove out Arvedui, the Last King of Arnor. Arvedui fled north, but eventually died up there. His son didn't take up the Kingship, and instead, became the first Chieftain of the Dunedain. Earlier, with the ending of the line of Anarion in Gondor, Arvedui (who was married to Firiel, the princess of Gondor) claimed the throne, since he was her husband, and of the line of Isildur. But, the stodgy old gits in Gondor wouldn't let him, and made Earnil, the victorious general, King instead. Anyway, that line also ended. These Numenoreans just didn't have any luck.

And that was why the line of the North never really claimed the throne of Gondor. After the death of Earnur, son of Earnil, his steward Mardil became the first Ruling Steward, and that line went on until the King returned at the end of the War of the Ring, and it was Aragorn who was the first King of the Reunited Kingdom of Arnor and Gondor.