A bizarre and funny movie, semi-based in fact. It was nominated for 10 Oscars, including Best Picture; although it didn't win any, it's still pretty good.
A brief opening scene sets up the situation: Irving (Christian Bale) and Sydney (Amy Adams) are obviously trying (and, initially, failing) to bribe Mayor Carmine (Jeremy Renner); they are in cahoots, but also in conflict, with Richie (Bradley Cooper).
How did they get here? An extended flashback describes Irving as a semi-respectable businessman with a chain of dry-cleaning establishments. He's also a small-time grifter, dealing in forged art and getting finder's fees for loans that he never actually gets around to finding. By chance he meets Sydney at a party; they bond over a mutual love of Duke Ellington. When Sydney finds out about Irving's criminality, she decides to team up with him.
All is well until they try to con Richie, who turns out to be an ambitious FBI agent. Instead of sending them off to the slammer for petty crimes, they decide to go after bigger game: corrupt politicians. Carmine is the initial target: he's the mayor of Camden, New Jersey. But it eventually involves the Mafia, putting everyone in danger.
Then there are personal entanglements: Irving is married to Rosalyn (Jennifer Lawrence); Richie and Sydney develop a certain attraction, which is aided by Irving's unsettled relationship with Rosalyn. Richie's superior (Louis C.K.) is also reluctant to go after the big game, and Richie persuades him through fair means and foul (including unhinged violence) to power through.
All the major characters are, to some degree, conning the others. But they're also somewhat sympathetic, so you're wondering: will any of them come out intact at the end?
Everyone involved is wonderful, giving a complex life to each character. In addition, if you want to see either or both Amy Adams and Jennifer Lawrence talk dirty in revealing garments, this is a pretty good choice.