Premillennialists believe the 1000-year reign of Christ mentioned in Revelation 20:5-6 (known as the Millennium) is literal and is yet to come. Postmillennialists believe the church will create a utopia (the Millennium) and it is yet to come. Amillennialists believe the Millennium is the church age, which started 2000 years ago and continues.

Since the 1000 years is mentioned only in the book of Revelation, the focus is on how Revelation should be properly interpreted. Most of the older denominations do not believe it is literal, or at least never talk about it. The Eastern Orthodox Church, for instance, teaches that the book of Revelation was added to the canon of scripture only on the condition that it would never be read in a public service. They still observe this rule today. There is no written record of this but the Muratorian Canon Fragment, (170 AD), states "We receive the Apocalypses of John and Peter only. Some of us do not wish the Apocalypse of Peter to be read in church." This may explain where the legend comes from.

Some teach Premillennialism, also called Chiliasm, was condemned as heresy at the council of Constantinople in 381, however the full record of the "Tome and Anathemas" of this council no longer exists. And there seems to be no other written record of this either.

Eusebius' Ecclesiastical history, 3:39 records Papias' (140AD) testimony that John the apostle taught him that Jesus would literally come back in the flesh and reign for 1000 years. 
Justin Martyr (165AD) was a disciple of Polycarp. Polycarp worked with John the Apostle in ministry for over 20 years. Justin states in his Dialogue chapters 32 & 110 that their would be a literal 7 year tribulation, and chapter 81 there will be a literal 1000 year reign of Christ.
Irenaeus (177AD), who also studied under Polycarp and  talked with John when he was young, teaches in his 'Against Heresies' 5:25-30 a literal tribulation and 1000 year reign of Christ. He goes on to say in 5:35 that Christians who try to allegorize these things are immature Christians.
Tertullian (202AD) taught in his 'Against Marcion' 3.5 that the 1000 year reign of Christ is real. 

In Eusebius' Ecclesiastical history (325AD) states in 7.25 the Gnostic Cerinthus started teaching not only is the 1000 years literal but it would be for gratifying the sensual appetites like, food, drink, sex, ect. This perverse teaching lead some early Christians to reject the book of Revelation and others to accept it but view the 1000 years as symbolic.
In Ecclesiastical history 7.24 we learn when allegorical interpretation became the normal style of interpretation Nepos, a bishop in Egypt, around 295 AD, wrote a book entitled "Refutation of the Allegorists" In which he interpreted the millennium as literal. This led some to think he was trying to revive the old teaching of Cerinthus. This caused more Christians to begin to hold to the millennium among other things as allegorical. Others began to avoid the issue all together.
Dionysius, in his "Promises," also mentions Nepos and Millennialism. ECF 6.81
Victorinus commentary on Revelation chapter 22 also mentions Cerinthus.

Eusebius (325AD) and Augustine (597AD) taught the Millennium was not literal. But remember at the council of Nicea, instead of taking the position that Jesus was homousos or heterousos, Eusebius tried to make a compromise stating Jesus was neither, which of course did not work. This shows his tendency toward avoiding the controversy. Augustan taught what would later be called Calvinism. All the first and second century fathers taught it was a Gnostic perversion to say man is not given a choice in salvation.

Several early church fathers teach the Millennial Reign of Christ would start in the year 6000 AM.

• Irenaeus (77 AD)
• Against Heresies 5.28