BioShock Infinite is not a direct sequel or prequel to previous BioShock games, taking place at a previous time and different setting, though features similar gameplay concepts from these games. The player controls a former Pinkerton agent, Booker DeWitt, as he attempts to rescue a woman trapped aboard the collapsing air-city Columbia in 1912. Like Rapture, Columbia is considered a failed utopia, but with signs present suggesting a theocratic government taking control at some point.
These are some of the screenshots available for the game so far. I am liking the change of setting and the bright out-door sun, it makes a stark contrast from the previous games. I am also interested in seeing more about the new direction they are going with this latest Bioshock game.