I intend there to be no real spoilers below. Something more spoilery will come along later, and properly flagged as such.
There's no denying that Days of Future Past is the most ambitious X-Men movie to date, stuffed full of ideas, overflowing with action, and almost exploding with characters, plot points and twists. That it manages to make sense is impressive enough, that it drives forward through all of the material without ever becoming boring is just two doors down the street from awe-inspiring.
The premise is simple and, for the most part logical. As we learn immediately, robotic Sentinels are hunting an apocalyptic world for mutants. One faction of X-Men on the run is able to keep ahead by using Kitty Pryde's special powers. Each time the group comes under attack, Pryde takes her fellow mutant Bishop to a safe place and projects his consciousness back a few days so he can warn them of the impending attack. Yes, this creates a pretty simple, familiar paradox, but nothing out of the ordinary.
But they can't run forever, and so Charles Xavier hatches a plan. Kitty Pryde should send somebody's conscience back further, to change history and prevent the roll-out of the Sentinels in the first place. It's decided that they'll send Wolverine back, which is pretty convenient, given that he hasn't aged between the early 70s and the apocalyptic future, allowing Hugh Jackman to play the role in both portions.
But there's a better reason for it to be Wolverine, and it's that this film is really all about Charles Xavier. Let me project my own conscience back a little and try to explain.
In the first X-Men movies, Patrick Stewart's Xavier is a positive, teaching influence on Wolverine. It's not fair to say he tamed him, but it's through their interactions that Wolverine came to be a respectable X-Man. You kind of have to disregard the Origins movie for that arc to really work at its best, but that's not much of a problem.
Now, it's Wolverine's chance to return the favour. He's sent back to a Charles Xavier who is an almighty mess, with his priorities all askew, and it's through this Charles' interactions with Wolverine – and, ultimately, the other X-Men – that he's going to get back in track.
Is there any hope of redeeming Magneto by altering history too? The possibility doesn't really come up, but Mystique definitely hangs in the balance. One key action of Mystique's is a pivot in the timeline and while she's disrupted from carrying it out more by force than by a change of heart, she's more than a plot point and her character development does become important.
I don't want to go too much further for fear of spoiling the story but I will say that, despite some stand-out action set pieces and some brilliantly inventive details – I particularly liked the last word on Magneto's possible involvement in the JFK assassination – what makes Days of Future Past work is the big picture. Stakes are established that are consistent with the characters as we know them, and these are explored in ways that remain narratively engaging as they unfold. At two hours and ten minutes or so this is far from the longest superhero film in living memory but it's not short and there was a real risk of it dragging. It certainly doesn't, though.
Oh, and yes, there is a post-credits sting that has nothing much to do with what has transpired and everything to do with what is coming next. More on that in the more spoilery review, though.