The historical Jesus debate, as we have seen, has three (or four) phases: the old quest (Reimarus to Schweitzer), the no quest of Bultmann and the new quest following Bultmann, and then what Tom Wright dubbed the “third quest” of the present day, though there are plenty of “new” questers still around. What is the 3d Quest?
First, it is concerned with a more positive appropriation of the Gospels and a less skeptical approach to them.
Second, perhaps most significantly, its driving force seems to be showing the Jewishness of Jesus and how Jesus fit into the socio-political currents of his day. A major criterion now seems to be “How does the Jewish world explain this fact about Jesus?” Some are calling this the plausibility criterion — how plausibly does Jesus fit into a Jewish world (and this sort of consideration when making historical decisions).

Let me sketch this a bit:
The era of Bultmann and the New Quest was concerned with separating Jesus from the Church in what is usually called the Jesus of history vs. the Christ of faith. The No/New Quest was not really centrally concerned with anchoring Jesus in his Jewish context. And what Jewish context was used was rooted in Strack and Billerbeck’s famous set than anything direct.
But, that era came to a halt with the discovery of the Dead Sea Scrolls and the revival of interest in 1st Century Jewish sources and the 1st Century Jewish context. Suddenly study of Jesus was being shaped by these discoveries. In the middle of the hey day of Bultmann a Welsh scholar by the name of WD Davies, famous for his Paul and Rabbinic Judaism, was one scholar who carried the torch for a more Jewish approach. But that was not the concern of Jesus scholars until the 50s and 60s.
Third, during the Bultmann era there was one major Jesus scholar who resisted Bultmannian hegemony in Germany and his name was Joachim Jeremias. He’s not often given the credit he deserves for the arrival of the Third Quest, but his famous book, NT Theology: The Proclamation of Jesus, was the climax of forty years of brilliant studies on Jesus.
Fourth, then came a flurry of major studies on the Jewishness of Jesus that in many ways built on and reacted to Jeremias:
G. Vermes, Jesus the Jew, deserves first place.
E.P. Sanders, Jesus and Judaism.
G.B. Caird, Jesus and the Jewish Nation and then later in NT Theology.
Two major students of Caird:
N.T. Wright, Jesus and the Victory of God.
M. Borg, Jesus: A New Vision.
Fifth, by the 90s the tide had turned. Everyone was trying to “outJewish” one another in their Jewish portraits of Jesus. I could list many other books, but these are some of the major players. Today most of us live and dwell and have our being in this Third Quest — this Jewish Jesus approach to the historical Jesus.
Still, the portraits are historical portraits and they are shaped by the distinction of the Jesus of the Gospels and the Jesus of history.