"Always in motion is the future..." --Yoda

Rating: 7/10 (15 November 2016)

Since this film is about humans being stuck in linear time, let's take first thing first. The premise: Aliens arrive in 12 ships, posted around the Earth. A linguist, Louise (Amy Adams) is recruited to go to the Montana location to help communicate with the heptapods (as these squid-like creatures are called). Joining her to head the project is a physicist, Ian (Jeremy Renner).
When Louise begins to decipher Heptapod B, the aliens' written language, she also begins to see flashes of her own life-- glimpses that the audience naturally assumes are memories: random scenes of her with her daughter, Hannah, including a conversation about her separation from the girl's father, and a scene of Hannah dying when she's still a schoolgirl.
But no, these are not memories, because it turns out Hannah did not exist before the aliens arrived. She is the daughter of Louise and Ian, who meet at the alien encounter. (Many reviewers, including Anthony Lane at The New Yorker, got this wrong. His review refers to the glimpses as flashbacks, but then admits he "hasn't worked it out yet.")
The key is the heptapod language, a kind of alien code that allows those who understand it to see the future but-- and this is also key-- not the *whole* future, and perhaps only your own future, at least not until you're fluent in heptapod. Louise gets glimpses of her future as she learns heptapod, and when she realizes that, she concludes that the aliens arrived to deliver their language as a gift: the ability to perceive nonlinear time, to glimpse the future.
She's half right. It is a gift to humanity, but the heptapods arrived, on what could well be a suicide mission, with a much bigger purpose. They're desperate. As Louise eventually learns, they have seen the future of their own civilization, and know a catastrophe is coming. They're here because they will need Earth's help.
The aliens and their perception of time as nonlinear is not developed. We learn little about them. Instead the basic theme-- communication as an aid to survival-- is explored through Louise, Ian, and their doomed daughter. The film has a lot of impressive CGI and sci-fi trappings, but at its heart, it is a family drama and-- to a greater extent than is needed, I think-- an action picture with rioting citizens, rival nations, and a bull-headed military.
It may be peevish of me, as someone who likes robust science in their science fiction, to wish there were less family drama and more about Time/Spacetime. But this is a thoughtful and well made film, powerful in places, and quite often suspenseful. I applaud the filmmakers for providing an escape from the question that arises when time becomes nonlinear-- If you know what happens in the future, are you free to prevent disasters? do you have free will?-- by giving Louise only glimpses, and random ones. She never sees the immediate future, so she doesn't know how the alien arrival will be resolved. Therefore she take a grave risk (which I won't reveal, because I still don't quite understand why or how she did what she did) which stops a military attack on the alien ships.
Now that I've written this, and thought about it, perhaps ARRIVAL deserves a higher score. I must see it again...