(1) Dispensationalist View: The Church replaces Israel. Dispensationalist George Eldon Ladd explains:
"The Greek word, ekklesia, is the word most commonly used in the Greek Old Testament to refer to Israel as the people of God. The very use of this word [in the Apostolic Writings] suggests that our Lord purposed to bring into existence a new people who would take the place of the old Israel....In the Old Testament era, the olive tree--the people of God--consisted of the children of Israel....[in the New Testament era] a new community has been formed...The Church is the community of the Kingdom of God...," (pgs. 112-121 of The Gospel of the Kingdom: Scriptural Studies in the Kingdom of God by George Eldon Ladd).
(2) Exclusionist View: The Church is composed of Gentiles ("the Gentile wing of the Ekklesia") and Israel (the Jewish wing of the Ekklesia). Gentiles are excluded from Israel. Dan Juster (UMJC) explains via diagram:
(3) Inclusionist View: The Ekklesia (Church) is the Messianic Kingdom of Israel, composed of Jews and Gentiles, who are equal partners in the covenants (see Eph. 2).