How did Smith get out of the Matrix?

At the end of The Matrix Reloaded and throughout The Matrix Revolutions, Smith is an actual human being outside of the Matrix. How did this happen?

Note: the question of why Smith didn't die at the end of the first movie is discussed here, but I am asking how did Smith get out of the Matrix and into a real body (so to speak)?

Answer

It's not explained. We've got a few choices though...

He's overwritten Bane's brain.

This one seems the least plausible; Smith has somehow managed to overwrite Bane's brain and implant his own memories and consciousness upon Bane's, in much the same way that the Agents overwrite bluepill humans inside the Matrix.

Obviously this opens up many unanswered questions but we do have the two canon examples such as the Steak Scene from the original Matrix film ("I don't wanna remember nothing") and from the Matrix webcomic "Goliath" where we see that the machines have the ability to edit memory. Presumably this control of memory would give them the ability to rewrite someone's mind that was jacked in.

He's inside Bane's implants

Bane, like all Matrix-born humans has ports implanted directly into his brain and body. We see Keanu interacting with the Sentinels while disconnected from the Matrix so presumably these ports have both wireless capability and some form of power source. It's not a great leap to imagine that they also have sufficient computing capacity to carry a copy of Smith's personality and that he's basically turned Bane into a meat puppet

This explanation also goes some way to explaining how blind Keanu can 'see' Bane as Smith during their iconic fight.

They're all still in the Matrix. Just on a higher level (MWAM)

Neo's ability to see Bane despite being blinded, Neo's ability to interact with the Sentinels despite not being jacked in, images of the future (showing Trinity's fall) on the monitor behind the Architect as well as Neo's ability to exist within the matrix despite being dead/disconnected all lend great weight to the suggestion that Zion isn't any more real than Capital City.

Since we see Agents moving freely into humans inside the Matrix, if we imagine that Morpheus' "desert of the real" is in fact simply another Matrix, it then makes perfect sense that Smith can move freely into a redpill human as they do into bluepill humans in a lower level of the Matrix.