What is the Relationship between Israel and the Church?

I'm going to discuss four different views: Dispensationalism,  Covenant Theology, Progressive Dispensationalism, and Historic Premillenialism.

Dispensationalist View

The church is new thing. So the church and Israel are separate and different. 

God has a plan for Israel.

God has a plan for the Church.

Romans 11: tells us the Jews were cut off the tree, and the Gentiles were grafted in. 

When Christ returns, Israel will respond and be grafted back into the tree. 

Right now we are in the 6th Dispensation, the age of Grace (Innocence, Consciouness, Government, Promise, Law, Grace, Kingdom.) It is a big Parenthesis, in God working with Israel. 

Progressive Dispensationalism

Some verses seem to hint that the Church is the True Spiritual Israel. This view changes the relation between the Church and Israel, saying that they are not quite the same, and yet they are. Gal 3:29.

They still believe in the Distinction between Israel and the Church. In the same way as the dispensationalist. The church will not go through the Rapture. 

Covenantal theology

Also called: Continuation, Replacement theology

God has one plan for his people. 

Israel has refused to obey, so God has replaced them with the Church. God has given up on Israel to replace them with the Jews. 

The church is the True Israel for today. (Rom 9:6). 

How do they then deal with Rom 11: 23, and the chapter which seems to talk of two different kinds of branches, the natural (Jews), and unnatural (Gentiles). 

Historical Premillenialism

This is a mediating position between Dispensationaism and Covenantal Theology. 

It does seem like today, the church is the Israel of today.

But God still has a place for Israel (Rom 11:23). 

People of God and church are still one so they will go through the Tribulation.