Christians don't usually know much about Jews, which has resulted in a lot of diversification in Christianity over the centuries. There are many extremely different kinds of Christians. Modern Jews do not seem to have a lot of interest in Christianity. Christians accept that Jesus can partially fulfill the prophecies until his return. Most modern Jews do not like that idea.
I'm not a modern Jew, however I think modern Jews expect Elijah to return and bring a restoration of everything that's been lost (check with them on the details). After Elijah does this, or perhaps along with Elijah will come a savior who will bring even more far reaching changes for everyone -- not just Jews. The savior will be as powerful a prophet as Moses was, judging with the same or possibly more authority. The savior will provide good laws for everyone everywhere -- not just for Israel. There is much much more to be said about it.
A Christian claims to be already part of a spiritually renewed world, a partial restoration or shadow of things to come that begins with John the Baptist. Christians consider John the Baptist to be a spiritual embodiment of Elijah, although not the actual Elijah, the man who must return. Views vary on this, but Elijah should literally return and Jesus should literally return as the scriptures indicate. That is when the restoration truly begins. Everything must still be restored that was lost, and it simply hasn't all been done yet.
Christians believe that non Jews can be added to Israel through means other than keeping all of the mitzvos and circumcision, by keeping the law of love through faith. This doesn't make non Jews into Jews, but something like that. There is much more to be said about it, of course. Modern Jews suggest this kind of conversion is unnecessary and perhaps impossible.
