It's very difficult to discuss this film without spoilers. The trailers give away some things: there's time travel, there are giant mutant-hunting robots, there's President Nixon. What follows shouldn't reveal any major plot-points, but might discuss a few details here and there. Hence, "spoiler-lite."
The film is based on a classic 1980 comic book story line that is followed in spirit more than in the details. In the dark and dismal future, mutants are hunted almost to extinction by giant robots called Sentinels. Through a bit of mutant legerdemain, Wolverine is sent back to 1973 to change the course of history. And then...
Well, after that it becomes a lot harder to discuss the plot without spoilers.
This is a successful movie on its face (it's currently at 91% fresh on Rotten Tomatoes, which is nigh-unto unheard-of; it even beats Captain America: The Winter Soldier at 89%). It's set to have the best opening weekend of any X-Men movie, and it's gotten terrific word-of-mouth.
First, the obvious stuff. I'm probably going to stop saying that special effects in films look great, because the film industry pretty much seems to have that down at this point. And they look great here. When we see people sliding along ice bridges, or lifting immense things through mutant powers into the sky, it looks like it was filmed for the news. (Although there is still a special quality that practical effects still have that seems to only be apparent when you see them and compare them to CGI in your mind's eye.)
The period pieces in 1973 are flawless. The clothes, the music, the "look" of 1973, are all spot-on. I swear it looked to me like they made the 1970's "fuzzy" intentionally to mimic the way it looks in documentaries, but I know I'm wrong. It just felt so right, and felt so in line with my own memories of the period (yeah, I'm old enough to actually remember 1973, barely).
Aside from the period pieces of music, however, I found the score somewhat... prosaic. We didn't have the stand-out Magneto theme from First Class, even when Magneto was being all "kneel before Zod" Magneto, which would have been a perfect call-back. And I found the mopey, self-pitying Xavier to wear a little thin, especially since the cause of his breakdown was almost non-existent. There's something in there relating to his telepathic powers, but they imply that that wasn't the reason that the school is in the state it's in, and that real reason is never adequately explained. The Vietnam war? Really? That's all we get? It hardly seems to rise to that level.
That said, the devices used to link the future and past segments were very well done. The theme of impending disaster in both timelines is well played, and there's some great foreshadowing from the beginning that gets played out at the end. Well done all around.
On the whole, I'd place this film high up in the X-verse. Probably second behind X-Men First Class, which I adored as a period piece more than anything else, which this film also captures. Whether it's better than the first X-Men is iffy; it's a larger film, and plays with the mythology in a very respectful and enjoyable way, but the first film did establish the mythology in the first place. Call it a tie. If the next film, X-Men: Apocalypse, is set in the 1980's and does a similarly wonderful job in-period, I'll be a happy camper.
There is shawarma after the credits; stay through them to see.