Actually, a variety of understandings of the “thousand year reign” – as found in the Book of Revelation – have existed for as long as the Book of Revelation has been around! (You can imagine the excitement as the year 1000 A.D. approached… )
However, in the 1800s, a new theological theory appeared from the pen of John Darby: dispensationalism. Dispensationalism, as you might know, is where the whole notion of the “rapture” was invented. Most dispensationalists believe in a literal 1000-year reign of Christ that follows the rapture and the tribulation.
However, dispensationalists aren’t the only ones who believe in a literal 1000-year reign. Catholicism, by contrast, takes on an amillenial stance: that is, the “1000-year reign” is not a literal reality.