While I do say next incarnation, BioShock Infinite is not a sequel in terms of story though. It is a bit more of a prequel, seeing as the game takes place about 30 years before Rapture was even built. That, and instead of taking to the seas by underwater city, the game takes place on a floating city (in the sky) called Columbia. Also not without its problems, this city is out of control - right at the epicenter of where it is floating, at that.
What it holds quite the same as the other two games is the overall story premise. A guy, Big Daddy counts on, shows up. Chaos is everywhere. He must find a way to get super powered in order to get a female(s) out of said city before it collapses on itself. Yes, there is more to it than that, but that is pretty much all that has been revealed about the story thus far.
While we wait for more details, here are the first few screen grabs and announcement trailer to hold us all over.