This entry in what will presumably be a trilogy hasn't started shooting just yet; production is scheduled to begin in September to meet a release date in May of next year.  Filming will take place principally in Los Angeles, with an additional sojourn to Tijuana that we're aware of. 

Returning director Todd Phillips wrote the screenplay with Craig Mazin, who contributed to the second movie.  Though that film, it was widely noted, stuck quite closely to The Hangover's formula, there seems to be a conscious effort at work to distinguish The Hangover Part III from its predecessors.  When the release date was announced, Phillips said, “I’m so excited to embark on another ‘Hangover’ film with Bradley, Ed and Zach. We’re going to surprise a lot of people with the final chapter we have planned. It will be a fitting conclusion to our three-part opera of mayhem, despair and bad decisions.”

The feral artwork below debuted on Legendary's Facebook.

Naturally, Bradley Cooper, Ed Helms, and Zach Galifianakis will be back as Phil, Stu, and Allen, and it's safe to assume Justin Bartha will also return as Doug, hopefully not quite so sidelined this time out.  Ken Jeong will also be back as the flamboyant criminal Mr. Chow, while Mike Epps will reprise his role as the other Doug from the first The Hangover.  How exactly of these characters fit into the plot is unknown.  Shortly after The Hangover Part II arrived theatrically, there was some talk that third film would find the Wolfpack breaking Allen out of mental institution, but we don't know if that remains the idea here.

The Hangover Part III is scheduled to hit theaters nationwide on May 25, 2013, the very same day as the sixth entry in The Fast and the Furious franchise.