The Twili in Twilight Princess are exiled Gerudo followers of Ganondorf cast into the Twilight Realm as punishment. Over 100 years, the realm affected them and they became the Twili. This explains the Gerudo symbol being all over the Twilight Temple, the absence of the Gerudo in TP, and the one portal to the Twilight Realm being located in the Gerudo desert.
Zant was the new 100-year male born to these exiled Gerudo-turned-Twili, but for whatever reason, Midna was chosen as the ruler over him, despite Gerudo custom. This is what led to his psychotic break, betrayal, and usurping of the Twili throne. It's also why Ganondorf was drawn to him, as another 100-year male.
As mentioned by Zant himself, he's resurrected by Ganondorf so long as the latter is alive, so he revives after being "popped" by Midna. This link is a two way street, so when Ganondorf is stabbed through the chest, it's the link to Zant, the other 100-year male Gerudo, that keeps Ganondorf alive despite his mortal wound. It's only once Zant severs the link (Likely due to hearing Ganondorf openly mocking and betraying him) with his infamous neck crick that Ganondorf truly succumbs to the wound and dies, the tie to his and Zant's mutual immortality arrangement severed.
As a result, Zant survives the end of Twilight Princess, hiding somewhere in obscurity, potentially to be revisited in a future Zelda game.
I subscribe to this one, with the added caveat that not all of Ganondorf's followers were Gerudo (think about how Ingo raised Epona to give as a gift to Ganondorf in order to curry favour). Besides, the Gerudo would have needed at least some men around to father the next generation.
Speaking of Gerudo, my headcanon is that after the events of OoT and MM, Link settled down with Malon and lived out his days Lon Lon Ranch.
Now the little-known thing about Malon is that her mother was likely Gerudo. Not only does she have the signature red hair, but when you speak to Talon with the Gerudo mask on, he says something along the lines of "I'm suddenly reminded of Malon's mother". This combined with the gossip stone that says "rumour has it that the Gerudo come into Hyrule Castle Town looking for boyfriends" and the way Gerudo romance works in BotW (Gerudo go out into the world, meet men, get married and/or have daughters, then return to Gerudo Town), implies that Malon was one of those daughters. Her mother is gone by the time Link meets her in OoT, but the clues as to her heritage are there.
Why is this important? Well, in TP, the Hero's Shade talks about his regret in having had nobody to pass his sword techniques on to before he died. Many believe that this is the very same Link from OoT/MM.Could this be because, married to a woman of Gerudo descent, he had no sons, only daughters? Living in patriarchal Hyrule rather than matriarchal Gerudo Town, it may have never occurred to him to teach his girls how to fight and they themselves may never have shown much interest, leading to the techniques becoming lost over time.
This isn't to say that TP Link can't be descended from OoT Link through the female line. The female-births-only thing the Gerudo display doesn't appear to be purely genetic. Otherwise we'd see families of red-haired women descended from Gerudo expatriates (like Ronson from BotW) all around Hyrule. Perhaps there's some magic at play in the desert that daughters of the Gerudo need to be in touch with to give birth only to daughters. Maybe it's cultural (thinking of the Terminan Great Bay pirates here) and it's the intervention of their goddess that causes this to be so.
Either one would put the kibosh on the Malon-only-giving-birth-to-daughters thing unless it's a coincidence or if Malon's mother happened to dedicate her at birth to the desert goddess, but Malon, being ignorant of her heritage, did not do the same for her own children.
I like to think it's true though.