"Blue is the Warmest Color" is a groundbreaking movie that should be seen by anyone with an interest in new ways of telling stories through film.
The movie's primary innovation is its absolute commitment to the faces of its characters. I've read reviews criticizing this as a "preoccupation with closeups," as if this were a lack of directorial balance, but that's ridiculous. What it is is pure intention. And brilliant invention. Somebody somewhere somehow got the idea to tell a story entirely through the faces of its characters, which is to say: entirely through the souls of its characters. And it works. The actors they found actually pull it off. The greatest burden was obviously carried by the relatively inexperienced star of the movie, but the camera dwells equally intently on the faces of all the other actors in their turn, and they don't fail the concept.
The other great boundary pushed by this movie comes from its willingness to sexualize and strip naked its young main character, not in the interest of titillation, but of authenticity. The sex scenes are the only times the camera strays significantly from the characters' faces (though even then, their faces receive more focus, and are more a part of the meaning of the scenes, than in most conventional sex scenes in lesser movies) but this is a natural extension of the commitment I wrote about above. To tell a story entirely through your characters' faces (and therefore their souls) is to tell the story entirely through their nakedness.
On these grounds alone, this movie deserves to be called great. Unfortunately, it is also flawed in a way that prevents it from being the masterpiece that some are making it out to be.
This flaw is not any "unlikability" on the part of the main character that critics have complained about. Or rather, the unlikability of a movie's main character is only a problem for a certain type of viewer. Some viewers (let's call them the Eberts) approach movies as artifacts, created works of art whose purpose is to convey some kind of poetry, usually using "real life" as a source of raw material. For them, the art is the thing. Others (let's call them the Medveds) want their movies to essentially be extensions of real life, to provide stories and people they can care about and enjoy in addition to the stories and people already in their lives. Within each camp, some will happen to like and/or identify with the main character of this movie and some will not, but it's only the Medveds that will interpret unlikable characters as an artistic failure on the part of the movie.
The actual flaw in the movie is not in the main character, but the story itself. It's a real shame that, having conceived of such a novel and daring approach to telling a story, the creators of this movie should use it to tell such an unoriginal one. As I watched the movie, I found myself thinking, "Here comes the scene that shows how dull her home life is," and "here comes the scene that shows her trying but not liking boys," and "here comes the [rather absurdly overwrought] scene where she faces hostility over her sexual evolution," and "here comes the scene that shows how she doesn't fit into her older partner's world," and "here's her partner getting too caught up in work and neglecting her." Etc., etc., etc.
This flaw, which would be enough to break most other movies, is, however, only a minor disappointment in this one. It would have been nice if Neil Armstrong had gotten his line right upon stepping onto the lunar surface ("That's one small step for a man") but no one thinks it detracted in any way from the accomplishment of pushing the boundaries of human exploration onto that new world.