The thousand years
Premillennial, postmillennial and amillennial readings, from the early chiliasts through Augustine to the dispensational schemes.
Revelation 20:1-6
1I saw an angel coming down out of heaven, having the key of the abyss and a great chain in his hand.
2He seized the dragon, the old serpent, which is the devil and Satan, who deceives the whole inhabited earth, and bound him for a thousand years,
3and cast him into the abyss, and shut it, and sealed it over him, that he should deceive the nations no more, until the thousand years were finished. After this, he must be freed for a short time.
4I saw thrones, and they sat on them, and judgment was given to them. I saw the souls of those who had been beheaded for the testimony of Jesus, and for the word of God, and such as didn’t worship the beast nor his image, and didn’t receive the mark on their forehead and on their hand. They lived and reigned with Christ for a thousand years.
5The rest of the dead didn’t live until the thousand years were finished. This is the first resurrection.
6Blessed and holy is he who has part in the first resurrection. Over these, the second death has no power, but they will be priests of God and of Christ, and will reign with him one thousand years.
What each tradition says
Rabbinic / Midrashic
Kohler says Jewish eschatology transformed the Perso-Babylonian world-year of twelve millenniums into a world-week of seven millenniums, matching the week of Creation. Psalm 90 suggested that the present world of toil, 'olam ha-zeh, is followed by a Sabbatical millennium, 'olam ha-ba', the world to come.
Kaufmann Kohler, in Isidore Singer (ed.), The Jewish Encyclopedia, s.v. 'Eschatology' (New York: Funk & Wagnalls, 1901-1906) — Eschatology, section 'A World-Week'
Patristic
Irenaeus says the righteous must first receive the inheritance God promised to the fathers. They will rise again and reign in this renovated creation, beholding God in it. Only after this does the judgment take place.
Patristic
Augustine says the devil is not bound throughout the whole time from Christ's first coming to the end of the world, the interval called the thousand years. He is not bound in the sense that during this time he shall not seduce the Church, for even when loosed he shall not seduce it.
Augustine of Hippo (354-430), The City of God (trans. Marcus Dods), in Nicene and Post-Nicene Fathers, ser. 1, vol. 2 (Buffalo: Christian Literature Publishing Co., 1887) — Book XX, ch. 8 ('Of the Binding and Loosing of the Devil')
Catholic
Kirsch writes that millenarianism was never held in the universal Church as an article of faith based on Apostolic traditions. He adds that the Middle Ages were never tainted with millenarianism, since it was foreign both to the theology of that period and to the religious ideas of the people.
Johann Peter Kirsch, The Catholic Encyclopedia, vol. 10, s.v. 'Millennium and Millenarianism' (New York: Robert Appleton Company, 1911) — Article, closing survey (on the Church's reception of Augustine's reading)
Orthodox
Dionysius says that some do not permit simpler brethren to have sublime and lofty thoughts about the glorious and truly divine appearing of our Lord, our resurrection, being gathered to him, and being made like him. Instead, they lead them to hope for small and mortal things in the kingdom of God, and things such as exist now.
Dionysius of Alexandria (c. 200-265), quoted by Eusebius of Caesarea, Eusebius, Church History, Book VII (trans. Arthur Cushman McGiffert), in Nicene and Post-Nicene Fathers, ser. 2, vol. 1 (New York: Christian Literature Publishing Co., 1890) — Book VII, ch. 24, §5 (Dionysius, On the Promises, quoted)
Reformed / Protestant
Matthew Henry reads the thousand years as reigning with Christ. Those who suffer with Christ shall reign with him in his spiritual and heavenly kingdom. This reign is a glorious conformity to Christ in wisdom, righteousness, and holiness, beyond what had been known before in the world.
Matthew Henry (1662-1714), An Exposition of the Old and New Testament, vol. 6 (Acts to Revelation), on Revelation 20 — Comment on Revelation 20:4-6 (the reign of the saints)
Evangelical
Barnes identifies the millennium as the long period when the principles of true religion will have ascendency on the earth. It will be as if the martyrs and confessors, the most devoted and eminent Christians of other times, appeared again and their spirit became the reigning and pervading spirit of all who profess the Christian name.
Albert Barnes (1798-1870), Notes, Explanatory and Practical, on the New Testament: Revelation (New York: Harper & Brothers), on Revelation 20:1 — Notes on Revelation 20:1-3 (analysis of the chapter)
Evangelical
Darby says Satan is not yet cast into the lake of fire but into the bottomless pit, where the legion of devils asked not to be sent. He is bound there so he cannot deceive the nations for a thousand years. During those thousand years there will be no seduction by Satan.
John Nelson Darby (1800-1882), Synopsis of the Books of the Bible (London: G. Morrish, 1860; complete-scan 'Hodgett' edition) — On Revelation 20 (the thousand years)