It's called the Millenium, Rev. CH 20.
The word Armageddon comes from Rev. 16:16 and describes the great battle for control of planet Earth just prior to the 2nd Coming. It will end when the Lord returns with the armies of Heaven to defeat the kings of the Earth (Rev. 19:11-21).
At the end of the 1,000 year Kingdom Age unbelievers will unite behind Satan in one final attempt to regain control of Earth. In that event the Lord simply sends fire from Heaven to destroy them all (Rev. 20:9).