Contains spoilers.
I expected this film to be called The Edge of Tomorrow, but there's actually no The at the start. Presumably it wasn't edgy enough. My only other complaint is that the invading alien life form are called Mimics when they don't look anything like humans and are just a mix of metal and monster. At no point in the entire film do they attempt mimicry.
Apart from these minor issues I enjoyed the film greatly. Within a few minutes you're right into the storyline and the momentum is kept up throughout. There's no slack at all, and every scene moves things forward or introduces something you're going to need to know later on. It's compelling viewing as you're always learning more about what's going on to the main character, played by Tom Cruise.
What's happened to him is this: he's an army bureaucrat who's been busted down to private and is now on the front line of the human army's big D-Day landing against the aliens. He's rubbish at fighting and dies, but gets splattered with a bit of glowing alien and so comes back to life at the start of the day he's just lived. This is the major sci-fi conceit of the film; that the aliens are magic and their power is now transferred to Tom Cruise. He keeps reliving this same day over and over again, going back to the start of the day each time he dies.
On one of his iterations he meets tough soldier Emily Blunt, who fortunately knows what Tom is talking about as she once experienced the same time-looping phenomenon, which let her become a hero before she lost the power. It's good that they meet, because it lets the plot proceed quickly as they discuss this strange thing that happened to both of them, and fill in the audience of the rules of the game. From them on it goes a bit like a computer game, with Tom continually dying but getting a bit further each time. There's no save points along the way, so he has to go through everything in the day each time, but of course this is heavily edited so we just see him making progress.
Since Tom's relived the same day so many times he effectively knows what's going to happen at all points, so it more or less seems like he can predict the future. This leads to some fun scenes where he anticipates what people are going to say, ducks punches with his eyes shut and so on. It's an entertaining notion, even if it's been done a few times before, notably by Tom Cruise in Minority Report when he's getting lead around by the Precog, and of course in Groundhog Day.
Initially Tom tries to explain to people what's happening to him, but no one believes him. Then he tries to just survive the beach landing, and finally teams up with Emily Blunt and tries to track down the alien superbrain and blow it up. Each time Tom dies the day resets, and he finds a new Emily Blunt and explains what's going on to her. My favourite scene is when he mysteriously finds some fresh coffee and a helicopter in an old farmhouse, and she twigs that although this is the first time she's experienced it, he's actually had this day loads of times before. There's also a nice bit where he gets sick of going to a warzone every day so gives himself a holiday and sneaks off to a London Pub (probably called London Pub) where some veterans' relatives chide him for deserting. Apart from these veterans there are many aspects of the film that remind you of WW2, with the distinct exception being that the German army is represented here by whirring tentacles, mini-godzillas and time-bending water brains.
The conclusion of the film is not as tight as the rest of it. There's some quick rule changes introduced about visions. The ones Tom and Emily were having are declared to be false, but if you are about to lose your time-looping power, or if you ram a plug into your leg, you get a true vision.
Any film with time travel is rather hard to end, as whatever conclusion you reach could easily be unwritten. You need something drastic and final to happen to show that all the time looping is definitely over now. This happens with them blowing up the alien brain, and for no good reason Tom now loops back two days. In fact, if I think about it some more I might find some other problems. Why does the alien power sync up with Earth days? Never mind. It was a very enjoyable film.