The emotional state that Like Crazy really nails is the mixture of elation, depression, and loneliness endemic to the long-distance relationship.
Drake Doremus' Like Crazy evokes a particular feeling with great effectiveness. The title implies that this feeling will be crazy, desperate, heedless love, and we get a little of that when we see Jacob (Anton Yelchin) and Anna (Felicity Jones) at the inception of their relationship during their final year of college. What may be “crazy” here is their close focus on each other, amplified by the film's own narrow view: what we know about each is limited to how they react to each other. But the context of their relationship remains fuzzy. It's easy to see that they adore each other, but trickier to understand why, apart from the fact that Yelchin and Jones are both attractive.
Following this meeting, the emotional state that Like Crazy really nails is the mixture of elation, depression, and loneliness endemic to the long-distance relationship. Most of the movie takes place during such a relationship; after a blissful year together (mostly off-camera), Anna must go home to England per her student visa, so she can return to Jacob a few months later. She makes the impulsive decision to stay the summer before flying home for a wedding; when she attempts to reenter the US that fall, though, she's halted at customs and sent back, banned until she gets her visa violation squared away. It could take years.
Jacob, meanwhile, sees his furniture-making business (semi improbably) take off, and is tied to Los Angeles for the foreseeable future. He can visit Anna on occasion, but they can't be together, not always, and not with the carefree passion of their first year. They try to make a long-distance arrangement work, agree to part, then try harder, stuck in a cycle just as irrational and youthful as their courtship, but a lot less fun.
In exploring this on-and-off relationship, the film does a decent job of making explanations for the distance that can't be bridged. Various characters suggest various solutions, none quite right; a green-card marriage, for example, doesn't prove as simple as it might in a studio romance. Like Crazy's willingness to deal with small, realistic, logistical problems in a relationship is refreshing in the face of much romantic contrivance and melodrama. The 2010 comedy Going the Distance made a similar but glossier attempt; it wasn't particularly funny, but it felt more honest than the average rom-com.
Like Crazy isn't particularly funny, either, and it's not meant to be, but some humor might have leavened the tone into bittersweetness, instead of the low-key dirge of its final 30 or 40 minutes. The couples' ups and downs in the first half turn to downs with a handful of ups in the second half; these events are well observed, but superficial and prosaic.
As the handheld shots get close, lingering on Anna and Jacob's faces to capture sad moments of longing, both characters remain somewhat opaque beyond their feelings for each other. While the movie plays fair in its depiction of two lives that can't be dropped for romance, an even better case could have been made if either of them had other friendships, or relationships that seemed like more than placeholders. Jacob meets a few nameless friends of Anna's during one UK visit, but he's only ever seen at his loft workshop or in a few scenes with his substitute girlfriend Sam (Jennifer Lawrence). I've read reviews suggesting that Sam is a better match for Jacob, but I wonder if this isn't projection based on Lawrence's innate likability and strength, held over from Winter's Bone and X-Men: First Class, movies where she actually has a character to play.
Apart from a few glimpses of Anna's parents (who may or may not have a drinking problem that the movie may or may not recognize as such), Anna and Jacob are the only real characters available in Like Crazy. Much of their relationship, especially their moments of connection, happens in montage, but Doremus' use of fast edits and time-lapse photography is often more expressive and exciting than the dialogue scenes. These start off naturalistic (reportedly, most of them were improvised) and then turn repetitive. (500) Days of Summer told a similar story of love and loss, with attention-getting technical flourishes to suggest the emotional swings. Like Crazy has the indie realness thing down pat. By the end, though, it could use some filmmaking creativity.