Advances have been made demonstrating the field of theology is indeed progressive and lively. One important advance that atheists like Dawkins need to address is medieval theology. You read that right, real cutting edge theology relies heavily on the Middle Ages. Thomas Aquinas and Scotus were both medieval theologians. 
|“||What, one wonders, are Dawkins’s views on the epistemological differences between Aquinas and Duns Scotus? Has he read Eriugena on subjectivity, Rahner on grace, or Moltmann on hope? Has he even heard of them? Or does he imagine like a bumptious young barrister that you can defeat the opposition while being complacently ignorant of its toughest case?||”|
How strong is this toughest case? Surely theologians like Eriugena, Moltmann and Rahner have built their cases on firm foundations? Surely New atheism can't prevail against modern Sophisticated theology? Errr well …. Atheists have demolished the very hardest case that Eagleton put forward in the above quote and it wasn't a big problem, just one example of how to refute it is given below.
|“||Eagleton misses the point. If a creator god doesn’t exist, it doesn’t matter whether the imaginary god’s grace is best described by Rahner or someone else. Besides, the millions of believers to which Dawkins writes have never heard of Rahner, either. Christianity as practiced by billions of people is not the Christianity of the academic theologians.||”|
PZ knows God doesn’t exist, there’s no elephant in the room. Still sophisticated theologians have made major advances discussing what color the non-existent elephant paints his toenails.  Surely theologians can do better than that one wonders.
Anyway advances were made when no one, apparently, was looking and the New Atheists resolutely fail to address this, plainly to their detriment.
Believing in God is ...
All of these developments clearly show that belief in a deity or deities is eminently defensible logically, philosophically, etc. Really, it's a shocking scandal that they haven't addressed these arguments, this evidence. Arguments such as... umm...
Well, we'll get back to you on that. But trust us, there's, like, hundreds of 'em, we're sure. Thing is, we must have left them in our other pants.
...oh, wait. Here's one. Atheists get in a fix because The One True God is invisible, and are terribly fond of saying things like: "The invisible and the nonexistent look very much alike." But from another perspective though, we actually do have proof – evidence – that The One True God is invisible: no one can in fact see Him!!!
Deny that, monkey boy.
What's more believers have a really sophisticate technique for dealing with critics. On Christian websites when we lose debates we delete the evidence. 
How to tell if it's really sophisticated theology
Somewhat more seriously--or roughly as seriously as the topic probably deserves--'sophisticated theology' is a little like that invisible God. You can tell it's sophisticated because you've never actually heard it. Or, to borrow a quote from the comments section:
|“||I use this handy metric: if you've actually heard it or read it, it's not Sophisticated Theology™. Sophisticated Theology™ cannot be explained because in doing so it would become open to refutation. Thus, Sophisticated Theology™, like the rainbow's end or a mirage, is forever beyond your reach. Rest assured though that ST™ is indeed what every believer really believes, no matter how much they may indicate that they—like Anthony Horvath—appear to have a slow preschooler's understanding of the world.||”|
—(Brownian, on Sophisticated Theology)
PZ can see through those sophisticated branches of theology that later vanish like a mirage. When rational atheists look closely into any theology the sophisticated stuff is somewhere else.
|“||I’ve noticed that whenever we focus on something specific in theology, it suddenly becomes by definition less sophisticated and the wrong argument to criticize). It’s still very, very wrong and deeply weird.||”|
Christians don't even try and show us any arguments that they insist prove God, they just blame us for not knowing them.
|“||Somebody somewhere is going to have to someday point me to some intelligent arguments for gods, because I’ve sure never found them. And I know, someone is going to complain that I always pick on the weak arguments…while not bothering to tell me what the strong ones are.||”|
Then ordinary Christians who've been taught unquestioning childlike faith assume they don't need to consider what the Gnu Atheists say. After all atheists don't know proper theology. Do they suggest specific theology we should read so we can point out why that theology is unsound? Of course they don't.
Gnu atheism is really problematic because new atheists understand philosophy as ordinary intelligent people understand it and write material that appeals to ordinary intelligent people. Naturally Christians would prefer atheists to use sophisticated reasoning that only advanced undergraduates, graduates and post graduates understand, fewer people would read the atheists and agree with them.
Believers rely on sophisticated incomprehensible theology to impress the masses and atheists really ought to keep what they write incomprehensible too.
Usefulness of theology
Jerry Coyne describes sophisticated theology as
|“||(…)a pile of garbage, steaming away in a dump of intellectual dishonesty. Its advocates make things up exactly like Less Sophisticated Theologians||”|
|“||(…) why we still have universities with theology departments, and haven’t razed them to the ground and sent the few remaining rational people in them off to sociology and anthropology departments where their work might actually have some relevance. It’s terribly uncharitable of me, but (…) I’m convinced that the discipline is the domain of vapid hacks stuffed full of antiquated delusions.||”|
Abandoning theology at universities would be simply unmitigated disaster. The world is in the middle of an unprecedented economic downturn. If theology is ended at universities how can those eminent theologians hope to find comparable employment elsewhere?
Telling sense from nonsense
Can theologians tell the difference between real theology and meaningless words jumbled together?
This was 'actually tested when a screed was presented at two theology conferences and theologians couldn't see it had no content. You feel that's somehow wrong? Academic theologians must be capable of telling meaningless words from real theology?
Complicated theology and woo
|“||Sophisticated Theology™ is merely a thin veneer of fancy academic words brushed onto the usual cheap plywood of fairy tales. In the end, it still comes down to theologians making stuff up to buttress a shaky faith against the onslaught of science and rationality.||”|
Sophisticated, however, does not mean correct. It merely means complicated. And every time one of their complicated arguments gets defeated (as is consistently the case), they got back and a few years later come out with a more "sophisticated" (read: complicated) version of the argument. Atheists await the next reincarnation of each piece of theology with the same excitement as an 8 year old in the Dentist's waiting room...
So, what is sophisticated theology and how is it different from unsophisticated theology? You can say there is no difference, they are both based on believing in woo woo, as Sam Harris once put it and none of it has anything to do with what is real. Jerry Coyne calls sophisticated and unsophisticated theology the, "theological sausage grinder" 
Sophisticated and relevant theology
Each sophisticated theologian argues that, "My personal theology is sophisticated and worthy of study. Atheists are at fault for neglecting it. By contrast other theologies that contradict the teachings of my religion, denomination or sect are clearly ridiculous and do not merit serious attention."
We don't need to study Astrology or the Stork Theory of Reproduction  in detail to dismiss them both out of hand. We don't need to study sophisticated theology in detail to see that Christianity doesn't make sense either. Roman Catholic theologians happily dismiss Protestant theology without studying it in detail, Christians dismiss the theologies of Judaism, Islam, Buddhism, Hinduism without studying all those theologies in any detail. Somehow atheists are to blame if we dismiss all theology the way believers dismiss alternative theologies.  
- Unintelligible theology
- Thomas Aquinas;Duns Scotus
- Nice list
- Luke Muehlhauser, the author is an ordinary blogger but the article cited has good philosophy and is well worth reading. The Courtier’s Reply, the Not My Theology Reply, and Straw Men
- Nice list
- Sophisticated theological arguments are unanswerable
- Sunday Sacrilege: Cant can’t
- Sorry, Vox, I don’t debate crazy pipsqueaks any more
- Walter Kaufmann on the gerrymandering of theologians
- Theology has no place in a university
- Theological inanity
- Another very Sophisticated Theologian explains why animals have to suffer
- The stuff that theologians believe!You can read a long quote from what Coyne calls 'shallow and devious rationalization' in the link.
- Intelligent Gestation Theory This by PZ is hilarious and well worth reading.
- Sophisticated Theology (Part 1) 1st part of a video that's entertaining and intellectually challenging
- Sophisticated Theology (Part 2)Equally good 2nd part of the video
- More sophisticated theology A large part of this is about how believers use sophisticated theological excuses for doing wrong, by PZ Myers
- Sophisticated theological arguments are unanswerable PZ shows when a Christian group couldn't answer arguments they deleted the thread.
- Myth: Atheist Critiques are Simplistic, Don't Understand Sophisticated Theology Christians expect atheists to follow higher standards than they follow themselves.
- Theology This is Atheism Wiki on Theology, it shows theology studies nothing real with quotes from Thomas Paine and Richard Dawkins.
- Sophisticated theology This is Atheism Wiki on Sophisticated theology.
- Sophisticated theology on RationalWiki
These two videos are entertaining, they will help you answer Christians who push sophisticated theology.
Beside the 1st 2 videos are quotes taken from the comment section.'
- Sophisticated Theology (Part 1) "I really enjoy your videos. Thanks for your work."
- Sophisticated Theology (Part 2) "You have perfectly captured the smugness, arrogance and scientific illiteracy of the average theologian. Great job!"