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1981’s X-Men storyline Days of Future Past didn’t actually invent the trope of the Bad Future (Dickens’ A Christmas Carol features one and that’s just the oldest one I can think of) but it may honestly be the single most influential use of that trope. Certainly in comics, maybe in general. If you’ve ever read a story where a character travels back in time to prevent a future with a purple sky, ruined buildings and too many damned robots, chances are it was influenced by this one X-Men story by Chris Claremont. It’s also one of the best-regarded X-Men stories in the franchise’s history, right up there with The Dark Phoenix. But whereas TDP is something of a weird digression, bringing in alien space empires and giant cosmic fire birds, Days of Future Past ties neatly into the X-Men’s recurring themes of prejudice (depicting a future where mutants are close to being wiped out) and the dangers of radicalism (Mystique’s assassination of a senator having brought that future about).

I’m not saying parables on racism can’t have giant planet-eating space-birds you understand, I’m just saying it’s a heavier lift.
Honestly, this one story’s impact has been so huge that if you actually go back and read it it can be a little underwhelming because it’s tropes and story beats have been copied so often elsewhere. Plus, the whole thing is wrapped up in one issue! They didn’t stretch it out across two years and have it cross over with every other Marvel title! What even the hell? But nonetheless it’s a story that is an intrinsically important strand in the X-Men’s big shaggy carpet and it was only a matter of time before the movies took a crack it.
The X-Men franchise is probably the most faithful to its source material of any superhero movie series and I don’t really mean that in a good way. Put it like this, Days of Future Past (the movie I mean) uses an incredibly convoluted time-travel plot to retcon away disastrous decisions made by previous creative teams. Just add a couple of Wolverine clones and Magneto revealing that he faked his death by pretending to be another villain who was pretending to be Magneto and you have the MOST X-MEN THING EVER. So at this point in the franchise the X-Men movies had been rescued from their Brett Ratner/Gavin Hood induced nadir and had been returned to their glorious prior status of being “quite good”. Brian Singer returned to the director’s chair with a mission; to integrate the previous “quite good” X-Men First Class and The Wolverine with his own X-Men movies thus creating one, unified timeline of acceptable quality.