The rest of the critics' answers:
"Because I'd rather not check and I'm fairly certain he's not that much older than me but below 40 I'll just say Alex Ross Perry ('Impolex,' 'The Color Wheel,' 'Untitled HBO Series'). I guess if I were really non-committed I'd say Lucas Cruikshank. Either of them."
"This is a toughie since the likes of Wes Anderson and Paul Thomas Anderson are now in their early forties. David Gordon Green has gone a little off-track recently but he was once a contender. Maybe Jason Reitman, particularly if he can slot in a couple of films of the same quality as 'Young Adult' before he hits the big 4-0."
"Among the under 40 crowd, I have to go with Jason Reitman. I'd consider him one of the ten best directors working today in general, so when you shrink it to those with impending midlife crises, Reitman really moves to the head of the class for me. He's also continuously improving, so he's also still one of the most promising young filmmakers around, which is a definite bonus."
"Alex Ross Perry."
"My pick would be Jason Reitman. He's only directed four films so far ('Thank You For Smoking,' 'Juno,' 'Up in the Air,' and 'Young Adult'), but they've all been home runs in my book. Reitman has the admirable ability to make movies that are commercial, but not mindless; emotional, but not manipulative; and funny, but not contrived. He is a true slice-of-life filmmaker. Plus -- for reasons I don't have time to go into here -- 'Juno' is my favorite movie of the past decade. I'm very excited to see where Reitman will go with the rest of his career."
"I'm a big fan of what Sarah Polley has been able to do over the last six years with 'Away From Her,' 'Take This Waltz,' 'Stories We Tell.' She has a great eye for cinema, likely influenced by working with directors like Bigelow, Gilliam, and Egoyan as a juvenile actor."
"Why 40? Of course, it's not good form to answer a question with a question. The dogs commented, 'What does it matter because you'd be dead in dog years.' I now also know that Matt Singer is all of 32. Not being particularly age conscious except in dog years, I checked the age of some directors who I might consider only to find that they (e.g. Joss Whedon and Ben Affleck) won't make the cut. Affleck at 40 is just barely out of the running, but he impressed me greatly with 'Argo' despite some minor historical quibbles. Whedon created 'Buffy the Vampire Slayer' and the TV series 'Firefly,' but it's the mad genius of 'Dr. Horrible's Sing-Along Blog' that really has me smitten. (Joss, No chance of being a groupie background extra for future episodes?)
By what seems no more than sheer luck, I've hit upon two directors: Rian Johnson and Jon M. Chu. If this question had been asked in late December, Johnson would have missed the mark. He is 39 now and best known for writing and directing that 2012 time travel movie 'Looper' which starred Joseph Gordon-Levitt as the young a regular Joe assassin and Bruce Willis as his older self in the future. The beauty of the intricate plot and its gruesome logic along with the seamless inclusion of a love story won me over. The gritty 1950s gone wrong in the future sensibility also charmed this fan of that dance era. Jon M. Chu, 33 but still dead in dog years, hasn't impressed me with his writing, but he understands dance and has good sensibilities in how he uses dance and records, including in 3D. I didn't watch 'Step Up 2: The Streets' for the plot or the acting. You knew how the story was going to play out pretty much after the first 15 minutes or so. The same can be said for 'Step Up 3D.' A purer expression of Chu's gift for recording dance and encouraging creativity is his online series, 'The Legion of Extraordinary Dancers.' I'm certain in the future, when dancers research aspects of today's dance and they will be turning to footage caught by Chu. In the interest of full disclosure, both Johnson and Chu attended the University of Southern California where they studied cinema. I also attended USC and will do so again."
"Just sneaking in there, I'm going to go with Rian Johnson. He only has three films, but I would count them all as great, plus each film is his own as a writer/director. On top of this, all of his films feel different and his craft has only grown stronger with each film/budget. Can't wait till he gets to make a 100 million dollar film."
"There may be young directors with more experience, but the one I'm most excited about is Xavier Dolan. His newest film, 'Laurence Anyways,' is a gorgeously filmed epic that establishes him as a major force. At just 24 he's already directed three films, and yeah he may be sort of an unknowing egomaniac in interviews, but that's par for the course with young geniuses."
"If one asked me a few years ago I would have certainly said David Gordon Green, but as of now it has to be Sean Durkin. He perhaps many not be the 'best' yet, but he holds the most promise with his stunning debut, 'Martha Marcy May Marlene' -- a film which I prefer over any other output from a current under-40 director. As for runner-ups, I can't wait to see where the careers of Cary Fukunaga, Edgar Wright, Rian Johnson and Jeff Nichols go."
"Sarah Polley. Sure, she's only made three movies, but each of them has been uniquely wonderful, and more importantly very different from each other. She's interested in the kinds of characters who almost never fit into conventional films, and she's clearly got a wide range of stories she plans to tell (including 'Stories We Tell,' which comes out soon)."
"I'm going to go ahead and take a two-fer here. Between the 36-year-old Cary Fukunaga ('Sin Nombre,' 'Jane Eyre') and the 34-year-old Sarah Polley ('Away From Her,' 'Take This Waltz') we've got both genders lined up."
"Even though I limited myself to only considering directors who have released at least three feature-length films, this still turned out to be an incredibly difficult decision. If you ask me (which you are), we are looking at the most talented crop of under 40 filmmakers of the last few decades, so this bodes quite well for the future of cinema. Mark Duplass (alongside his over-40 brother, Jay Duplass) ended up being the most consistent of the young directors on my final list. Though I still consider the Duplass Brothers' first two features -- 'The Puffy Chair' and 'Baghead' -- to be their best films to date, I have truly loved all of their five of their features. Oh, and I have a couple of honorable mentions: Joe Swanberg and Frank V. Ross."
"A couple of years ago, I'd have said Paul Thomas Anderson, but he's passed the 40-year threshold. There are still a number of impressive contenders to this title, but I'm going with Edgar Wright. Over his first three films, he's tapped into a generational ADD mentality without going so far overboard as to alienate the audience. His ultra-fast pacing coupled with rapid-fire visual and verbal humor, as well as a running theme of the man-child being forced to grow up (if only slightly) have proved a winning combination through riffs on zombie films, action movies, and cult horror. Hopefully 'The World's End,' his upcoming capper to the trilogy that began with 'Shaun of the Dead,' is as enjoyable as what he's made already."
"The problem with choosing a favorite young director is that their body of work is so limited. Guys like Steve McQueen, Jeff Nichols, and Andrew Dominick all have good films, but I don’t think any of them have hit their stride yet. But if I have to choose a director under 40 that has some consistency, style and potential, I’ll go with Jason Reitman. 'Thank You For Smoking,' 'Juno' and 'Up In The Air' (I wasn't a fan of 'Young Adult') were all good to great films and as Reitman develops his style even more, I think he's going to develop into a great director."
"I'm going with Lisandro Alonso, that deadpan Argentinian explorer. His interest in the mysteries of isolated landscapes and their closed-lipped residents, whether in the icy windswept climes of Patagonia ('Liverpool') or the sweltering jungle ('Los Muertos'), revived the creatively adventurous spirit of Robert Flaherty, setting the stage for the flood of doc-fiction hybrids to come. It's been five years since 'Liverpool,' but he's working on a film with Viggo Mortensen now that is my most anticipated film of whichever year it comes out.Tentatively titled 'Sin Titulo,' an early summary described it thusly: 'Time and space utterly blend together and become suspended around a dog that mutates until it turns into what may be the very enigma of creation.'"
"There isn't another director under 40 producing more exciting work than writer/director Derek Cianfrance has though his first two (released) feature films. He shows a passion to tell personal stories about unglamorous people and places, real people I can recognize, and exactly the ones most others have no interest in depicting. His films and characters exude an often raw, emotional truth that is unmatched. He offers plenty of style, with huge Scorsese and Cassavetes influences, but his focus is clearly on characters, which is why he gets such quality actors giving beautifully naturalistic performances. Four years ago I didn't know who Derek Cianfrance was and now I'm not sure there is a director whose next film I more eagerly anticipate."
"I'm gonna say it's a tie between my pals Lucky McKee and Rian Johnson."
"No symbolism, no foreshadowing, no filmic tricks to manipulate the audience into believing sentimental rewriting of personal histories for the director of 'Goodbye First Love' or 'Father of My Children.' Mia Hansen-Love paints a picture of time and adolescent longings in as real a film about first love as it gets. She never gives information, she creates a mood and colors a moment. I remarked to Hansen-Love at the 2011 New York Film Festival about her painterly use of colors, specifically the way she positions objects and clothes in reds, blues, and whites. She was happy that I did not mistake it for metaphor, as it is the sensual quality that makes her place a red bikini in front of a bright blue summer sky. She referred to Eric Rohmer, who once said, that every film has a color. 'Obviously, this one is red.'"
"Rian Johnson gets in just under the wire, as he turns 40 in December of this year according to Wikipedia. I think his debut 'Brick' is one of the top 10 films of the '00s, and it would probably be enough to make him my favorite even if 'The Brothers Bloom' and 'Looper' were not also great."
"The best director under 40 is Jeff Nichols. He has only three films under his belt, but they're all fantastic and with a distinctive voice. 'Take Shelter' is a goddamn masterpiece."
The Best Movie Currently In Theaters on May 6th, 2013:
The Most Popular Response: "The Place Beyond the Pines," "Upstream Color." (tie)
Other Titles Receiving Multiple Votes: "Something in the Air," "To the Wonder," "Iron Man 3," "Post Tenebras Lux," "Spring Breakers."