United States directors best known for their quirky comedies like Fargo and Raising Arizona; the brothers write their own scripts and alternate top billing for the screenplay. Joel gets credit for directing the films, but the two brothers work so closely together and share such a strong vision of what their film is to be that actors report that they can in fact approach either brother with a question and get the same answer.
The Coen brothers' humor is a combination of dry wit, exaggerated language, and glaring irony; the brothers frequently use dialogue to develop characters and advance plot. Their characters sometimes make educated comments (as in Tom's "if I'd known we were going to cast our feelings into words, I'd have memorized the Song of Solomon") but more often make pretentious comments: ("Jesus, Tom, I was just speculatin' about a hypothesis" (Miller's Crossing), "You know, it's proven that cigarettes are carci--carci--cancer-causing" (Fargo), and The Dude's imitation of Maude's "in the parlance of our times," appending it with "You know?... Man?" (The Big Lebowski).)
The Coen brothers storyboard their films extensively before starting filming; they state that it helps them get the budget they want as they can show where most of the money will be going. The Coens used Barry Sonnenfeld as cinematographer through Miller's Crossing; then Sonnenfeld left to direct his own films and has had some success at it with The Addams Family, Get Shorty, and, most notably, Men in Black. Roger A. Deakins has been the Coen brothers' cinematographer since Sonnenfeld's departure.
Visually, the Coens favor moving camera shots, especially tracking shots and crane shots; when the camera is "static" it is in fact almost always still drifting slightly. Occasionally in their tracking shots they "rush" the camera forward, as in the scene in Raising Arizona where Nathan Jr. is discovered missing; the camera's rush forward is a tribute to their longtime friend and director Sam Raimi, who directed Evil Dead (which Joel Coen helped edit). (Raimi also helped write The Hudsucker Proxy, which the Coen brothers directed; and the Coen brothers helped write Crimewave, which Raimi directed.) The Hudsucker Proxy features not one but two consecutive rushes when Norville shows Mussburger's secretary the Blue Letter: first on the mouth of the lady screaming on the ladder, and then on Norville reacting to the scream.
The Coen brothers use camera angles which sometimes hide rather than reveal information, as in Fargo when Jean Lundegaard is hiding in the shower, in Miller's Crossing when Tom goes into his room after Leo leaves, (Verna is on the bed behind him), and in Blood Simple when Abby is sitting up in bed with Ray and the Volkswagen pulls up outside her window. They also frequently "hide" their cuts in a close-up on an object, a la Hitchcock's Rope: one occurence of this is obvious in Fargo, when Carl is banging on the television to get it to work (when the picture finally comes in clearly it is in fact a cut to Marge's television as seen from her bed); a similar tactic is used in Miller's Crossing when the close up of the window at Vernie's house pans away to show a man dead on the floor at another; in The Hudsucker Proxy when Amy Archer is cheering "Go Eagles!" after getting hired on by Norville, which cuts to her showing the same thing to her coworker at the newspaper; and in Blood Simple when the "close-up" of the ceiling fan over Marty's head at the bar turns out to be from Abby's point of view on the couch at Ray's house.
Stylistically, Coen Brothers movies show a heavy debt to film noir, featuring stark contrast in lighting (most notably in Blood Simple, Miller's Crossing, and Fargo) and the typical theme of people being in over their heads in a scheme. Their movies tend to deal with kidnapping, and use misunderstanding as a plot device (misunderstanding over who killed The Rug and who took his hair causes friction between different mobs in Miller's Crossing; misunderstanding of Norville's blueprint causes him some grief later in The Hudsucker Proxy; everyone except for the nihilsts in The Big Lebowski misunderstands about Bunny's kidnapping; and in Blood Simple, misunderstanding is the driving force behind the entire plot past the thirty minute mark.)
The Coens also show a fascination with both blood and vomit; Miller's Crossing, Barton Fink, and Blood Simple all show elaborate puddles of blood, whereas in Fargo it's a wide spray in the snow coming from a wood chipper; Tom vomits in Miller's Crossing once off-screen at his house and once on-screen in the crossing itself; Marty vomits in Ray's yard in Blood Simple, and then vomits again on the floor later (but this time it's a torrent of blood); Charlie vomits off-screen in Barton Fink; and Marge bends over to vomit but doesn't in Fargo. The Coens also, for whatever reason, prefer not to put the opening credits at the very beginning of the film.