In the replacement theology model of understanding scripture, supported by early church "fathers" such as Justin Martyr and Origen, God has changed his chosen people from ancient Israel to the New Testament Church.
The replacement theology model, therefore, asserts that "the chosen" can include not only Israelites but also Gentiles (non-Israelites) as well. This model also teaches the covenant God made with Israel at Sinai (the Old Covenant) has been abrogated by the New Covenant delineated in the New Testament.
In a variation of the replacement model, the Roman Catholic Church believes that it is the "new Israel" who has superseded the Old Testament's chosen people.
Dispensationalism, as opposed to replacement theology, states that God is not yet done with Israel as his chosen people (as per Romans 11:1). They believe the Jews, or even Israelites in general (including what many refer to as the "Lost" tribes of Israel), are still God's people.
Today, one of the chief ways this theology (and dispensationalism) becomes politically controversial is when Christians take sides concerning the legitimacy of the modern state of Israel in the Middle East.
While replacement theology has and continues to be widely held by those who consider themselves Christians, a number of denominations are either moving away from or have rejected this template for understanding scripture.