Carl Sandell’s review published on Letterboxd :
I don't understand how the Coens manage to make stories that appear cynically dark but infusing them with a warmth and humor. This story of a singer-songwriter with a romanticized self-image is a hilarious tribute to struggling artists and the way they can sabotage themselves. Llewyn Davis writes nonsensical lyrics as he hasn't lived anything to write about, since that would cramp his artistic style and not let him live. This type of warped self-image is standard for the Coens but it always feels fresh and creates intriguingly complex protagonists. These characters always bring out the best of the actors and it's hard to imagine that Oscar Isaac will ever top this performance.
The story about this kind of spoiled artist in New York is very popular these days, but the Coens add a cute spin by placing the story in the 60s and have Llewyn go around the artsy Greenwich Village. This period also sets up the key component of the movie, the wonderful folk music. It's probably hard to fully appreciate the movie if you don't enjoy the music, even if it is presented somewhat sarcastically.
As always the movie is filled with a gallery of colorful supporting characters. Compared to other Coen films it's a pretty bland group, but chances are they can grow upon rewatch. There is so much depth to the story with every interaction bringing out a new wrinkle to Llewyn Davis. And as is usually the case things end up pretty much where they start but we are wiser and happier for having been brought around for the ride.