Amongst Christian theologists, there exist three popular beliefs regarding eschatology: premillennialism, postmillennialism, and amillennialism. In the broadest sense, the concept of millennialism in Christianity refers to the general belief that in the future, a Golden Age will come in which Jesus will return (Second Coming) to reign for 1000 years over the earth, concluding with the final judgment of mankind. However, there are a variety of different outlooks as to the specifics concerning this generalized timeline.
Premillennialism is the belief that, put very simply, Jesus’ return will precede the establishment of God’s earthly kingdom. This means that Jesus will physically rule the world from a throne, most likely located in Jerusalem. However, premillennialism itself may also be subdivided into two categories: historic and dispensational. Historical premillennialists believe that the establishment of this earthly kingdom will occur following the Great Tribulation. The Great Tribulation is a period of time in the future when people across the world will face terrible disasters, wars, and famines, resulting in the deaths of most of the earth’s inhabitants. Historical premillennialists therefore believe that Christians of the earth will be subjected to the miseries of the Tribulation, and will be forced to endure persecutions until such time that Jesus shall return (Second Coming) and establish a Godly kingdom on earth. To be more specific, Jesus is said to return and battle the Antichrist (who rules the world during Tribulation) in the battle of Armageddon; Jesus and his followers will be victorious, and establish the earthly kingdom. Dispensational premillennialists, on the other hand, believe that Jesus will return one day and make the Christians of the earth - both living and dead - ascend to heaven, an event also known as the Rapture. Following the Rapture, all non-Christians will be forced to endure the Tribulation, after which Jesus will return from heaven with all the world’s Christians to establish a 1000 year reign on earth ("1000 years" should not be given much literary attention - it is more likely to represent a long period of time than an exact interval).
Postmillennialism is the belief that Jesus’ return will occur after the establishment of God’s earthly kingdom. It is thought that the forces of Satan will eventually be overcome by the forces of good, and Christianity will spread across the world by virtue of the victory celebrated by the faithful. Only then will Jesus return to reign over the world.
Finally, amillennialism is the belief that God’s earthly kingdom will not feature the physical presence of Jesus on a throne. It is believed here, instead, that this kingdom of God will be spiritual in nature, and that following this long period of sustained spirituality across the nations, the final judgment of mankind shall be established.
Regarding the connection of Jews to Christian eschatology, the most important sect is dispensational premillennialism. In this sect, a clear division is made between the Church and Israel. Israel is interpreted in the writings much like it is interpreted in today’s political world - as an ethnic nation of Jews. The Church, on the other hand, is the diverse body of individuals who have come to accept Jesus. As such, the Rapture will only include the Christians of faith, as all other people of the earth (including the Jews) will be forced to remain behind and endure the Tribulation. Here, it is said that of the Jews remaining on the Earth, two-thirds will die, and the remaining third will be left in Tribulation to preach to the world that Jesus is, in fact, Messiah (the one-third remaining Jewish population figure is from Zechariah). Another book (Revelation, final book of New Testament) says specifically that 144,000 Jews will remain in Tribulation to spread the message of God to the unbelievers. These Jews will be pious and without fault before the throne of God. The reason why Israel as a whole is not saved in this belief system is because the inhabitants of Jerusalem (the Jews) must be cleansed from impurity and sin. Mind you, this is what the dispensationalists believe, who happen to constitute, from my understanding, the majority of Christians in America and are essentially the heart of Christian Zionism. Others think Zechariah does not refer to millennialism at all, but instead to the sack of Jerusalem by the Romans.