Cersei Lannister seized the ultimate revenge and successfully destroyed The Sept of the Seven with most of the high court inside of it. Tommen was spared but is ultimately so overcome with grief that he commits suicide. So who is the king now on Game of Thrones? The lineage gets tricky.
Tommen doesn't have an heir (meaning a son), his siblings are dead, and all of Robert Baratheon's siblings are dead. So it can't be a Baratheon. Stags are out. Margaery could have tried her hand at being a solo queen, but she bit the dust in Cersei's wildfire party, dying in the massive blaze at the Sept of the Seven. So did Lord Tyrell and Loras Tyrell. The only Tyrell left is Olenna, who is down in Dorne. As Vulture points out, Robert technically was able to unseat The Mad King because he himself had a tiny bit of Targaryen blood in him, thus legitimizing his claim to the throne. Basically, he was just Targaryen enough to take over. If the successor must have Targaryen blood, then Danaerys is obviously the next rightful queen. But, we also confirm in this episode that R + L does, in fact, = J, so Jon Snow is also a Targaryan descendent who could take the crown, though he's technically a bastard.
Finally, one devoted Redditor crawled back through Robert Baratheon's family tree and found that one of his ancestors married a Lannister, and their descendants carry on the Baratheon line in the Lannister family. So, by that measure, Jaime has a claim to The Iron Throne, since his father Tywin is dead, and Jaime is no longer a member of The King's Guard. (Thus, he is able to inherit lands and titles.) Occasionally, in such messy cases, the realm invests in a little democracy and calls a Great Council, made up of all the lords of Westeros, who vote on a new king. In this case, it would have been a smart idea to breed some good favor and loyalty. Sadly, it seems loyalty died out in The South with Ned Stark.
While plenty of people could and likely will continue to try and take The Iron Throne, before the Season 6 finale ended, we saw the crown placed upon Cersei's head. She is named Queen of the Realm, apparently since she's the only "Baratheon" left, and there's no High Sparrow left to sentence her to death for incest anymore.
So, for now, Cersei is our rightful queen.