How do the people of God in the Old and New testaments relate to one another? There are three popular views on this, which I shall vastly oversimplify here:
Dispensationalism - God has two peoples, one in the Old testament (Israel) and one in the New testament (the Church). The promises made to Israel in the Old Testament will be fulfilled literally during a thousand-year reign of Christ in the future.
New Covenant Theology - God has two peoples, but the promises made to Israel were ultimately fulfilled spiritually in the Church, which is a greater Israel. There was always a remnant of true believers under the Old Covenant and the Church is the continuation of this true, believing remnant.
Covenant Theology - God has one people, called Israel in the Old Testament and the Church in the New Testament. The only difference between the two is that the levitical priesthood have been replaced with a greater high priest, Jesus, resulting in a change of law and the inclusion of the gentiles.
I veer somewhere between Covenant Theology (CT) and New Covenant Theology (NCT), though I am closer to the first of the two. Here's what I make of each of them:
Dispensationalism - Though there are many solid evangelicals who hold to this, it does seem to imply that there are two ways of salvation. This pits the two Testaments against each other.
NCT - Basically correct when it comes down to the law (admittedly this is its main concern), however it seems to underemphasise the unity of the Old and New Covenant peoples of God.
CT - Pretty much correct, though I take issue with the idea that the Ten Commandments all still apply today. The Sabbath command was only valid under the levitical priesthood, our rest is now found exclusively in Christ, who is our new and greater High Priest.
And here is what the law of the New Covenant, the law of Christ, is really about: