I read this book several months ago, and I’ve enjoyed subsequent discussions about it:
Kevin DeYoung and Greg Gilbert. What Is the Mission of the Church? Making Sense of Social Justice, Shalom, and the Great Commission. Wheaton: Crossway, 2011. 
Here’s how D. A. Carson recommends it:
Among the many books that have recently appeared on mission, this is the best one if you are looking for sensible definitions, clear thinking, readable writing, and the ability to handle the Bible in more than proof-texting ways. I pray that God will use it to bring many to a renewed grasp of what the gospel is and how that gospel relates, on the one hand, to biblical theology and, on the other, to what we are called to do.
Ed Stetzer’s Themelios review is critical, but I generally agree with DeYoung and Gilbert on this one.
Related:
1. TGC discussion (11:43)
2. Desiring God interview with Scott Anderson (1:44:55)
3. 9 Marks interviews with Mark Dever
5. Review by John Starke
6. Kevin DeYoung and Greg Gilbert, “Some Answers to Some Nagging Questions”
7. Kevin DeYoung and Greg Gilbert, “One More Time on Good Works and the Mission of the Church”
8. Kevin DeYoung and Greg Gilbert, “A Response to Ed Stetzer’s Review of ‘What Is the Mission of the Church?’”
9. Justin Taylor, “Responding to Stetzer and Critics on the Mission of the Church”
10. Kevin DeYoung, “The Mission of the Church in Living Color”
11. Collin Hansen, “Mission Critical”
Thanks for pulling these together. I’m looking forward to reading the book in a few weeks (I’ll be writing a review for EMQ next summer). From what I’ve read from DeYoung before and reading through the reviews thus far, it seems that a (the?) critical issue is the distinction between the responsibilities of the church qua church and those of individual Christians. DeYoung and Gilbert are arguing for the mission of the institutional church as distinct from that of individual Christians. Thus, the institutional church’s mission is the Great Commission not the (2nd) Great Commandment, which is to be fulfilled by Christians. The critical reviews don’t recognize this distinction, so they lump these together into the mission of the “church” (i.e., all Christians), then criticize DeYoung and Gilbert for neglecting the fuller mission.
One other note: I found it interesting that Stetzer critiqued them for not being up on missiological thinking. From everything I’ve seen about the book, it’s foundation is the exegesis of Scripture to determine the mission of the church. Stetzer’s remarks reinforce a feeling I’ve had for a few years now–missiology mostly ignores/assumes biblical backing and focuses on sociology, anthropology, etc. Instead of asking “what does Scripture have to say about our thinking and strategy?” the question too often is “what has worked or what do we think will work?” Thus, when someone comes offering a biblical argument, the response is not “here’s where the exegesis is flawed” but “that’s not the focus of our discussion.” Though I may not be considered qualified to speak to these issues, I find that disturbing.
Let me pile on with Ben and say “thank you” as well for linking these all together in one spot. I read the book when it first came out and was thankful for the biblical priority evident throughout. It was clear all the way through the book that exegesis preceded the forming of philosophy and methodology (as much as is humanly possible).
And from that standpoint it seems that most criticisms are being launched against the methodology aspect rather than its foundation in the exegesis. This in and of itself is suspect.
On another note I was ,at first, surprised that Carson, as the editor of Themelios, would publish Stetzer’s negative review of a book that he endorsed. And then I thanked God for a man humble enough and tolerant enough (not to mention his many other obvious gifts) for his evidences of faith and trust in Christ. Not used to that.
I watched video above and it seems to me that Kevin and Greg are making an artificial divide between the mission of the institutional church and the Christian life. The institutional church is made up of individual people, so without people there is no institution. If the people are behaving badly, the “institution” of the church will not be heard when “it” proclaims the gospel. It will be dismissed and ridiculed for being hypocritical and/or judgmental by the very people they are attempting to reach.
It seems to me that we need to start examining the complementary, symbiotic, and balanced relationship between making disciples (institutional) and the Christian life (personal)because they are mutually dependent on each other. Oversees missionaries are already well aware of this.
Loving people, providing for the needy, protecting the marginalized, and living upright lives grants an individual and an institution the respect needed to proclaim the gospel and make disciples. When done over and over, the DNA of the city will change, the culture will change, and history will change. Shalom will then be a realization, rather than just an aspiration.
As I read Scripture God has sent us to (his mission for us):
1) Glorify himself and enjoy him forever.
2) Love God and others.
3) Proclaim the Gospel to salvation and for sanctification.
4) Provide for needy and protect the marginalized.
5) Make disciples by teaching them all that he commanded.
6) Live upright, godly, and self-controlled lives in the present age.
All in the context of community (institutional).