JayQ’s review published on Letterboxd:
Unquestioningly auteurs, the Coens work within a few recognizable structures: the Western noir (Blood Simple, No Country for Old Men), the screwball caper (Intolerable Cruelty, The Ladykillers, Burn After Reading), and the hero's journey (True Grit, O Brother Where Art Thou, Inside Llewyn Davis). The latter may be the case for this present film, but the brothers turn the mythic journey arc on its head by asking, "what if the hero does not acquire a boon bestowing power by his journey's end?" What if the journey simply continues anew, becoming an endless loop? Llewyn Davis becomes the unenviable hero, one who is made directionless by grief. "What are you doing?" reads a scribble on a bathroom stall in the film, an existential question that Davis appears to approach in perpetuity. Though he may lash out in his depression, Davis is as empathetic a character as the Coens have ever devised, crippled by the uncertainty that lingers after the passing of a loved one.
Intelligent, as well as auteurs, the Coens carefully layer these motifs throughout the film (Ulysses, the wayward cat, being the primary example), creating a melancholic musical that sings honestly from the broken heart.