At the conclusion of the millennial reign of Christ, unbelievers of all time will be raised and judged. Their resurrection is the resurrection of judgment spoken of by the Lord in John 5:29. Their judgment will take place before a Great White Throne (Revelation 20:11-15). Their Judge is the Lord Christ (see John 5:22,27).
11 Then I saw a great white throne and the One Who was seated upon it, from Whose presence and from the sight of Whose face earth and sky fled away, and no place was found for them.
12 I [also] saw the dead, great and small; they stood before the throne, and books were opened. Then another book was opened, which is [the Book] of Life. And the dead were judged (sentenced) by what they had done [their whole way of feeling and acting, their aims and endeavors] in accordance with what was recorded in the books.
13 And the sea delivered up the dead who were in it, death and Hades ( the state of death or disembodied existence) surrendered the dead in them, and all were tried and their cases determined by what they had done [according to their motives, aims, and works].
14 Then death and Hades ( the state of death or disembodied existence) were thrown into the lake of fire. This is the second death, the lake of fire.
15 And if anyone's [name] was not found recorded in the Book of Life, he was hurled into the lake of fire. AMP
22 Even the Father judges no one, for He has given all judgment (the last judgment and the whole business of judging) entirely into the hands of the Son,
23 So that all men may give honor (reverence, homage) to the Son just as they give honor to the Father. [In fact] whoever does not honor the Son does not honor the Father, Who has sent Him.
24 I assure you, most solemnly I tell you, the person whose ears are open to My words [who listens to My message] and believes and trusts in and clings to and relies on Him Who sent Me has (possesses now) eternal life. And he does not come into judgment [does not incur sentence of judgment, will not come under condemnation], but he has already passed over out of death into life.
25 Believe Me when I assure you, most solemnly I tell you, the time is coming and is here now when the dead shall hear the voice of the Son of God and those who hear it shall live.
26 For even as the Father has life in Himself and is self-existent, so He has given to the Son to have life in Himself and be self-existent.
27 And He has given Him authority and granted Him power to execute (exercise, practice) judgment because He is a Son of man [very man]. AMP
Those judged are simply called "the dead"-unbelievers (in contrast to "the dead in Christ," which refers to believers). This judgment will not separate believers from unbelievers, for all who will experience it will have made the choice during their lifetimes to reject God. The Book of Life that will be opened at the Great White Throne judgment will not contain the name of anyone who will be in that judgment. The books of works that will also be opened will prove that all who are being judged deserve eternal condemnation (and may be used to determine degrees of punishment). It is not that all their works were evil, but all were dead works, done by spiritually dead people. It is as if the Judge will say, "I will show you by the record of your own deeds that you deserve condemnation." So everyone who will appear in this judgment will be cast into the lake of fire forever.