Rey asked in a comment on this post what the New Perspective on Paul is, and I decided my response was worth a whole post.
It's a three-stage thing. It started with E.P.Sanders in the 1970s, who argued that people have too harshly criticized first-century Judaism as legalistic and works-based salvation. He described the view not as earning a place in the covenant by works but as getting in the covenant by grace and staying in by works. There's general agreement now that he selectively picked evidence to support that, and the Jewish picture in the first-century was not monolithic. At the same time it's also not clear that this notion filtered down to the average person anyway. Still, there were people who said what he described the whole of first-century Judaism as believing, and it was significant enough that you have to be aware of that as you read Jesus' criticisms of the Pharisees and Paul's description of his past and the Jews in Galatians, Romans, and Philippians.
Stage two was James Dunn, largely in the 1980s. His Romans commentary (Word Biblical Commentary) is a key location for much of this work, but he's got a few monographs on this general perspective as well. His chief addition to Sanders had to do with interpreting Paul's use of the term that we translate in English as "works of the law". Since the Reformation, most Protestants have taken this term to refer to actions done to earn salvation in accordance with the Torah. Dunn says the works of the law in Romans are not simply doing what the Torah says. It's about the distinctive markers of the Hebrew people in the Torah, not the whole of the law.For Dunn, Paul is saying that you don't become a Christian by becoming a Jew, so relying on Jewish identity markers is contrary to the gospel. It's not about reliance on works.
A number of scholars have considered this too reductionistic, because one of the things Paul talks about is those who disobey the law as the Gentiles do. So whatever the works of the law that can't save are, it's got to be more than just ethnic identity markers. Those who try to obey the law aren't necessarily saved, but neither are those who break the law, because disobedience to the law is grounds for judgment.
The third tier of the New Perspective comes from N.T. Wright. Wright doesn't accept everything in Sanders and Dunn, but he accepts some of it. Generally, he accepts their portrait of first-century Judaism but rejects their picture of what drove Paul. His contribution seems to me to be primarily in criticizing the standard Protestant interpretation of justification as imputed righteousness. In his view, the atonement is very much a legal matter, but it's legal vindication first and foremost. He doesn't deny imputation, but he doesn't see it as central. There's also reconciliation, but that's a result of the vindication before God. See this lecture for Wright's own account of his general views.
I think the jury is still out on Wright, partly because so many reactionary types misunderstand him, as he makes pretty clear in the paper I just linked to. I'm much more amenable to him than to Sanders or Dunn. I think they both go way too far, though even Wright thinks that. I suspect Wright steers too far from imputation in order to emphasize some things Protestants have ignored, but I think he's probably right to complain that these things get ignored. Douglas Moo and John Stott are the only Romans commentaries in my list by traditionalists on this issue, I believe, that deal with this issue strongly. Joseph Fitzmyer and Leon Morris completely ignore it as if it's a brief fad not worth their time. See Mark Heath's comments on these two authors' takes on this stuff: Moo on the New Perspective; Stott on the New Perspective.