THERE WILL BE UNMARKED SPOILERS IN HERE

Liz (who at one point was named Anna) is Booker’s daughter and Booker is Comstock from the past to the future to the past again, he lost his daughter and led to the creation of infinite timelines and infinite Bookers and Elisabeths. They are also protagonists/antagonists from the other *shock titles. Also the lighthouses somehow have the power to cross time and space.

The remains of Columbia that sunk to the bottom of the ocean floor may or may not be the base of Rapture. Songbird was basically a prototype Big Daddy.

Booker is a horrible parent.

There are so many fucking questions after that ending.

Here's how I understood it:

Booker is born, grows up, and takes part in the massacre at Wounded Knee while he's in the Army.

Booker has daughter, Anna, but when asked where she came from he can't come up with an explanation.

Booker takes up drinking and gambling to ease his guilt over what happened at Wounded Knee, and amasses a substantial debt.

Booker is approached by a representative of a wealthy industrialist who offers to buy his daughter in exchange or wiping out Booker's debt. Booker agrees, but at the last moment tries to go back on the deal. He's unable to get his daughter back and carves her initials into his hand as a form of penance.

Booker's guilt and depression become worse and he turns to religion. He's baptized and takes a new name, Comstock.

Comstock decides to live in Columbia, where he becomes a major political/religious figurehead.

While living in Columbia, Comstock works with another group of people on a time machine/gateway to parallel universes. An unforeseen side effect of this work renders Comstock sterile, but the project is a success and the machine works.

Still feeling guilt about his decision to sell his daughter and now unable to have any more children, Comstock travels back in time/space and buys Booker's daughter. He brings her to Columbia and gives her a new name: Elizabeth.

The Booker from the past who just sold his daughter goes through the same religious conversion but rejects baptism at the last moment. He's later approached by the Luteces (I missed why), who bring him into the dimension where Elizabeth/Anna now lives. The process messes with Booker's memories and he fabricates the "Save the girl, wipe out the debt" scenario from what little pieces of information he managed to retain.

Booker goes through the events of the game with Elizabeth, which results in the destruction of Columbia. Elizabeth's/Anna's accident (her finger getting cut off as the portal closes) back when Booker originally sold her is what gave her the abilities to see into other worlds/timelines (the tears). With the the device that was limiting her powers is destroyed as well, she's able to see that by Booker purchasing her from himself, he's created an endless series of time loops/universes where the events will play out again and again and again.

The Elizabeths/Annas bring Booker to the exact moment where he is no longer the man he was before the baptism, but is not yet one of the two men he will eventually become. They drown him there, sealing off the loops and preventing the whole mess (and themselves) from existing in the first place.

What I don't understand is the post credit scene. Has the loop not been broken, or is a new path/chance available, or what?

@bocam: I don't think it's that tightly tied into the other Shock games. The lighthouses are representative of the different dimensions, but it's more a metaphor than anything, a visual aid that Elizabeth is producing to help Booker understand it. I certainly don't think that Columbia under the ocean is Rapture, they're stories being told in two different dimensions. I've seen several people on these forums under think just how "infinite" the multidimensional thing truly is.

I don't buy that Booker and Comstock are the same people. Here are some thoughts:

• If Comstock is buying Anna from Booker (something you'd assume he'd pretty explicitly aware of) then why would he rename her Elizabeth. What function does that serve?
• Why is Comstock so old? Elizabeth is supposed to be around 19 years old, putting her date of birth at about 1893 (the same year that Columbia made it's debut at the Chicago World's Fair). If Booker and Comstock are the same dude, that means that Bookers pre-Columbia timeline(the 'flashback room') would have happened back in the 1950's or so with Elizabeth being born in at about the same time and pulled forward to the 1890's when Comstock takes her from Booker. Now, admittedly there's no evidence to dispute that this is the case, but not much to suggest it is the case, either.
• Booker served at the Wounded Knee Massacre. This is a real life thing that happened back in 1890. And it was clearly young Booker that served then because, hey, our protagonist remembers it. That means that his Baptism had to happen sometime after 1890, probably after Elizabeth's bith in 1893*. If Booker and Comstock are the same person, then why does Comstock age 50 years whilst Booker only ages 20.
• The struckout point above: Booker must have been baptised before Elizabeth was born because otherwise, how is it that killing Booker kills the Elizabeths? This pretty much kills the whole Comstock thing for me entirely, because it means that Booker would need to undergo a whole other spiritual awakening to become Comstock, and that just seems unlikely to me.

Just my observations. I personally am still choosing to believe that when Booker says that he's both he and Comstock, that he's being metaphorical about that fact that they both abandoned Elizabeth, to some extent.

I have seen the post credits part on YouTube and I have replayed the final moments twice now but in my game it never gives me the post credits part. Just goes to the credits and when I hit a button shows the infinite logo and back to the main menu .... Weird

In the interest of keeping the numerous Bioshock Infinite plot threads to a minimum, I'm going to lock this thread and direct everyone here.