What is the nature of this judgment? There are a lot of questions about this, but there are also a lot of speculation as Scripture does not seem to say how exactly the saints will judge angels. Most seem to think that this judgment will consist in approving the judgments of God made against the fallen angels and the wicked.
At The Parousia
The Bible also teaches that the Last Judgment will take place at the coming of Christ, on the last day, that is the only time indication that the Bible gives (Matt. 24:36). 2 Thessalonians 1:5-10 tells us that we will be granted relief “when the Lord Jesus is revealed from heaven with his mighty angels” (v. 7), but He will not be granting relief to everyone. Rather, the Holy Spirit says that He will be revealed “in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus” (v. 8), through which they will suffer “eternal destruction” (v. 9), and that will happen “when he comes on that day to be glorified in his saints” (v. 10). Notice that on a singular day and with the same singular Parousia of Christ, two opposite things happen: His coming brings joy and relief to His people, but it also brings eternal destruction and misery to those who do not know the gospel of our God. This is the Final Judgment at the Second Coming of our Lord. 1 Corinthians 4:5 connects the time of judgment with the coming of Christ saying, “Therefore do not pronounce judgment before the time, before the Lord comes, who will bring to light the things now hidden in darkness and will disclose the purposes of the heart. Then each one will receive his commendation from God.” The time for judgment is after the Lord comes, and when the Lord comes He will bring to light the things now hidden. John 12:48 says that the judgment will take place “on the last day.” Matthew 25:31ff begins with the coming of the Lord in glory before going into the Final Judgment. The Day of the Lord is often connected with judgment, which is the day on which Christ will return (see here for more). There is a day and an hour fixed by God for the revelation of His perfect justice, which will certainly come and men should live with the knowledge of that. If they are outside of Christ, they have no hope, but if they are in Christ they will have confidence on that awesome day (1 John 4:17).
The Standard
God will judge the world by His own standard. He is His own standard. 1 Samuel 2:3 says that “the LORD is a God of knowledge, and by him actions are weighed.” He is the standard that determines what is right and what is wrong. The Law which He has given us in the Ten Commandments—the moral law—is a reflection of His morally excellent character and the standard which we will be judged by. God is the Judge and He will do no one any wrong, for He is Just (Gen. 18:25). The Bible repeatedly declares that God is just and He will judge the world by righteousness (e.g., Ps. 9:7-8; 96:10-13). He will not be bribed or be partial in His judgment (Rom. 2:9-11), but will give each man according to his works. No man outside of Christ can have any confidence of fulfilling God’s righteous standard or co...