The real novelty is Putnam's response, based on the causal theory of reference or content externalism or something like it (I'm fuzzy on this point). I hope I can do it justice from memory.
He argues that because the brain in a vat has never had the appropriate sort of causal contact with external objects, its thoughts don't refer to them. So the brain has whatever brain states go on in me when I think "the sky is blue", but it has never seen the sky, and so its mental states don't refer to the sky. They refer to something else. Probably some disjunctive property of however the apparatus stimulates the brain's nerves (it's really hard to say what this is). It turns out then, that the brain is not falsely believing/failing to know the facts that we might think about by thinking "the sky is blue", it's accurately representing some other kinds of facts. So that type of scepticism is self-undermining, because it attributes thoughts to the BIV that it couldn't possibly have.
I should add that it seems to me that while this argument is tremendously creative, it belongs to a whole strand of philosophy from the 80s that seems to have died out. There's a decent chance you'll read some Putnam, but AFAIK people aren't publishing much on his BIV argument (though people use the example of a brain in a vat sometimes).
[0] Arguably, Descartes posited that the deceiver could deceive you about anything, including logical relations, while the BIV case just involves people giving you misleading sensations, so that's one conceivable difference in the discussions, but that's not a point that I ever saw anyone discuss in detail. It matters for Descartes scholarship, but that's all.
http://plato.stanford.edu/entries/skepticism-content-externa...
EDIT: I got Putnam wrong. There is still the theistic difference though.