When our Lord comes to this earth, His primary purpose will be to set up and begin His new Holy kingdom. But to do that it will be necessary to renew the earth and its people. Thus all unbelievers will be judged and killed.
Before the Lord comes to personally judge the nations, it appears from Zechariah 14:2 that He will allow the armies at Armageddon to fight each other.
For I will gather all the nations against Jerusalem to battle, and the city will be captured, the houses plundered, the women ravished, and half of the city exiled, but the rest of the people will not be cut off from the city (Zech. 14:2).
And a plague will be upon them so that their flesh will dissolve.
Now this will be the plague with which the Lord will strike all the peoples who have gone to war against Jerusalem; their flesh will rot while they stand on their feet, and their eyes will rot in their sockets, and their tongue will rot in their mouth (Zech. 14:12).
This sounds to me like chemical warfare or nuclear warfare. Also, The Lord will bring a great panic upon them, so that they will start fighting each other.
And it will come about in that day that a great panic from the Lord will fall on them; and they will seize one another’s hand, and the hand of one will be lifted against the hand of another. 14 And Judah also will fight at Jerusalem; and the wealth of all the surrounding nations will be gathered, gold and silver and garments in great abundance. 15 So also like this plague, will be the plague on the horse, the mule, the camel, the donkey, and all the cattle that will be in those camps. (Zech. 14:13-15)
It sounds like what happened a few times in the Old Testament. (1 Sam. 14:15, 20; Judg. 7:22; 2 Chron. 20:23).
Some scholars believe that during this time of panic and confusion is when Jesus will come and touch down on the Mount of Olives and split it in two, thus allowing believers to escape.
And in that day His feet will stand on the Mount of Olives, which is in front of Jerusalem on the east; and the Mount of Olives will be split in its middle from east to west by a very large valley, so that half of the mountain will move toward the north and the other half toward the south. 5 And you will flee by the valley of My mountains, for the valley of the mountains will reach to Azel; yes, you will flee just as you fled before the earthquake in the days of Uzziah king of Judah. Then the Lord, my God, will come, and all the holy ones with Him (Zech 14:4-5)!
Now after the Lord comes, He will intervene personally. First, He will take hold of the beast and the false prophet, and will throw them alive into the lake of fire (Rev. 19:20). Next, he will kill all the rest of the unbelievers (who have come to Armageddon) with a sword which comes from His mouth. This language seems to be symbolic, meaning that He will execute them merely by speaking.
And I saw the beast and the kings of the earth and their armies, assembled to make war against Him who sat upon the horse, and against His army. 20 And the beast was seized, and with him the false prophet who performed the signs in his presence, by which he deceived those who had received the mark of the beast and those who worshiped his image; these two were thrown alive into the lake of fire which burns with brimstone. 21 And the rest were killed with the sword which came from the mouth of Him who sat upon the horse, and all the birds were filled with their flesh.
Now after Satan is locked up in the Abyss (Rev. 20:1-3), this, I think, is when all the remaining living humans on the earth, believers and unbelievers, will be gathered before Christ on His throne (Matt. 25:31-46). Here Christ will separate believers (the sheep) from the unbelievers (the goats). All unbelievers will go into eternal punishment, but all righteous believers will enter the kingdom and will be greatly blessed by the Lord for 1000 years.