Recently a friend asked me about dual covenant theology. As I see it, dual covenant theology starts with two Scriptural premises:
1) That God's covenants with the Jewish people are enduring/eternal.
2) That God has acted to benefit the world through Yeshua of Nazareth and the new covenant he instituted.
The first premise is generally understood as the revelation preserved in the Jewish tradition, while the second premise has been preserved within the Christian tradition.
Dual covenant theology is an attempt to simultaneously affirm both of the above premises. Specifically, it does so by asserting that the "new covenant" established by Yeshua was and is specifically for the Gentile nations (who, until then, had been without a covenant relationship with God), while, for the Jews, the way of salvation is by remaining faithful to God's revelation in Judaism (i.e. the Torah, Moses, etc). In other words, Dual Covenant theology says that Jewish people have no need for the gospel of Yeshua since they already have a relationship with God.
While it seems to me that Dual Covenant theology has received most of its attention due to the Jewish-Christian dialogues of the past 50 years, many see its antecedent in the views of the medieval Jewish sage Maimonides, who affirmed the possibility that both Christianity and Islam were being used by God to bring the Gentile nations to monotheism.
However, dual covenant theology is hardly a unanimously affirmed position among participants in Jewish/Christian ecumenical relations. Other Jewish and Christian scholars recognize that the original message of Yeshua and his apostles was directed to both Jews and Gentiles and that to frame it as "God's message only to the Gentile nations" is to distort the original message of the New Testament authors.
That last sentence sums up my position--at least according to how I've defined Dual Covenant theology. However, this is one of those topics that can be confusing to talk about and requires a lot of defining of terms. (This is usually the case with discussions about "covenants".) I see Dual Covenant theology as a flawed attempt to harmonize the two Scriptural ideas above. Messianic Judaism encompasses an alternative approach.
Unfortunately, many Christians mistakenly see any affirmation of the Torah's enduring covenantal significance for the Jewish people as necessarily a form of Dual Covenant theology. This is, in my opinion, a miscategorization (probably stemming from the mistaken conviction that the only proper Christian perspective towards the Law is one of supercession/abrogation.)
However, if Yeshua of Nazareth lived as a Jew faithful to the Torah of God and taught his apostles to do the same (Matt 5:17-20), then it seems today's followers of Yeshua ought to also affirm the continued place of the Torah as "the inheritance of the assembly of Jacob." (Deut. 33:4) And if the apostle Paul was able to say, about unbelieving Israel, "to them belong the adoption, the glory, the covenants, the giving of the law, the worship, and the promises; to them belong the patriarchs, and from them, according to the flesh, comes the Messiah, who is over all, God blessed forever" (Rom 9:4-5), then today's adherents to Paul's gospel ought to also strive to affirm the enduring nature of God's covenants with the Jewish people.