The complex yet emotional alien drama “Arrival” will have you scratching your head and wiping your eyes in equal measure. Amy Adams commands every scene in this intelligent, thrilling film unlike any other — a story that hinges on a female scientist’s intelligence and empathy as the key to potentially saving humanity, and also weaves a profound personal story into the narrative. The only bad thing I can say about “Arrival” is that it makes you realize how one dimensional so many other films are.

This is Adams’ film, and for “Arrival” to have been nominated for “Best Picture” while she was left out for “Best Actress” is absolutely insane, and with Emma Stone winning, even more so.

Adams plays Dr. Louise Banks, a brilliant linguist called upon to communicate with aliens when 12 identical spacecraft land across the globe, with unknown intentions. Even while facing the most awesome spectacles of space and time, Adams doesn’t overact while radiating pain and wonder, both intimate and universal.

Unlike many science fiction films, “Arrival” takes time to develop its premise. As Dr. Banks and her associates, including Jeremy Renner, work their way through communicating with the visitors, it is believably laborious and detailed.

The envoys of scientists and their military escorts enter the huge spacecraft through an opening in which gravity works differently and they walk sideways up the walls. Inside, they encounter huge squid-like aliens that make noises but primarily communicate through a floating ink substance with which they write.

Any film or story this removed from our reality is going to have to take some huge jumps, but “Arrival” is more convincing than most. Indeed, some viewers might feel it takes too much time convincing and hope, during a few lengthy middle scenes, for a nice, implausible jump in the characters’ comprehension to scoot things along. However, this is a journey worth taking, so just sit tight through the linguistics scenes.

While the film focuses on Adams and Renner’s efforts to understand the aliens floating right above the United States, international conflict ratchets up the suspense. Chinese and Russian governments threaten global war, stock markets go into freefall, and looting and chaos are rampant. With this terrifying scale in the background, the quiet power of Adams’ intelligent and graceful performance holds the center. The emotional resonance of her personal loss echoes so beautifully through this story, and is so satisfyingly important in understanding the plot twist.

The solution to the film’s mystery is a twist but not a gimmick. It is not so much clever as intelligent and profound, and will leave you thinking about it for quite some time. Unlike a flashy mindbender along the lines of “Inception,” this film has an incredible story but also an incredible meaning. It engages the head and the heart in equal measure, and is deeply moving on both levels.

“Arrival” is currently available to rent.