Is the idea that there will not be a future literal 1000 year reign of Jesus Christ upon the earth. (Revelation 20:1-6). The Latin prefix a means “no” while the term millennium is Latin for 1000 years – Amillennialism thus meaning “no 1000 years”.
The term Amillennialism denies the actual presence of a future literal 1000 year reign of Jesus Christ on earth after the second coming of Christ, where as Premillennialists believe this is still to happen. Having said that, Amillennialists do have their own version of what they believe the millennum to be; it’s what they reject though, and that is the idea of a future literal 1000 year reign of Jesus Christ on earth.
According to Amillennialists, their version of the millennium is our currently present age, before the return of Jesus Christ. So the millennium or Kingdom of Kingdom of God if you will is right now, as we speak, being fulfilled spiritually.
Amillennialists will tell you that their millennium began with the resurrection and ascension of Jesus Christ and will end when Jesus returns again to establish the Eternal Kingdom that is spoken of in Revelation 21-22.
Satan is currently bound and Christians believe it or not are enjoying the benefits of living in the millennium and that the Saints are reigning in heaven. They also claim that 1000 years is an indefinite period of time and is not a literal 1000 years, so when does their millennium end? Well your guess is as good as mine.
During this millennial time-period there are trials and tribulations, even though Jesus and His saints are ruling from heaven. Jesus will then return to earth again of which there will be a resurrection of all the saints and judgement will take place. Then the Eternal Kingdom will begin.
Premillennialism (belief in the Rapture) was the predominant view for the first 300 years of church history. I have been told so many times that this is not true, and that the Rapture is a new teaching. I have also been told that the Roman Catholic church hold to the teaching of the Rapture, but this is completely false. The Roman Catholic Church are AMILLENNIAL.
Saint Augustine (354-540) is often referred to as the FATHER OF AMILLENNIALISM. He abandoned the correct Premillennial teaching for a false Amillennial teaching. It was Augustine who falsely interpreted Mark 3:37 to be a ‘present age’ binding of Satan. (If only someone had bound Augustine, we would not be in this mess). St. Augustine viewed the Catholic Church to be the visible form of the Kingdom of God. Augustine saw that the millennial reign of Christ was taking place IN and THROUGH the church (including all it’s creeds, sacraments, offices, etc, etc, etc). In his book, City of God, Augustine promoted and praised Amillennialism.
Because of Augustine, Amillennialism quickly became the NEW view of the church. It was then later adopted by Protestant reformers like Martin Luther and John Calvin. Some Anabaptists continued to hold onto Premillennialism.
Premillennialism thankfully experienced a huge resurgence over the last 250 years, but still to this day comes under fire. Unfortunately the Word of Faith movement got hold of this teaching and because of this Premillennialism takes another beating.
Amillennialism is the official position of the Roman Catholic church, and is held by many Lutherans, and Reformers. The Roman Catholic church’s rapture is at the end of their millennium.
Early history regarding Premillennialism.
D. T. Taylor tell us that the earliest denouncement of Chiliasm was in A.D. 373 by Pope Damascus.  C. Cooper notes that, “From the third to the fifth centuries Chiliasm was vigorously fought and ruthlessly put down, although it was not officially declared a heresy. It was all really rather awkward, because previously nearly everybody of note had been a Chiliast… Between Chiliasm and the charge of heresy stands the canonization of Justin the Martyr and Irenaeus.” 
So as we can see Premillennialism is not a new idea. It might seem new to some only because the gospel truth is shining it’s light out in the open again after being trampled upon by the Roman Catholic Church.
———Notes:  C. Cooper, “Chiliasm and the Chiliasts,” Reformed Theological Review 29 (1970): 12  D. T. Taylor, The Voice of the Church on the Coming and Kingdom of the Redeemer; or, A History of the Doctrine of the Reign of Christ on Earth, rev. and ed. H. L. Hastings (Peace Dale, RI: H. L. Hastings, 1855), 115.