One of the key elements that is emphasized in the Old Testament laws is that taking personal revenge was forbidden for the Israelites (see Lev. 19:18; Deut. 32:35). The Old Testament laws exacted ‘just’ punishment for all offenses: “life shall be for life, eye for eye, tooth for tooth, hand for hand, foot for foot” (see Exodus 21:23-25). So, for any offense that was committed in those days, the accuser and the accused were required to “stand before the Lord, before the priests and the judges who serve in those days” (v. 17) as the plaintiff and the defendant.
God’s desire for us clearly is not to judge others and exact personal revenge, and this was stressed to a greater degree all through the New Testament. We are instructed to "repay no one evil for evil" (Romans 12:17). Taking this a step further, God has told us specifically not to judge others: "Judge not, that you be not judged. For with what judgment you judge, you will be judged; and with the measure you use, it will be measured back to you." (Matt 7:1-2) Instead, we are required to forgive others when they wrong us, so that our Heavenly Father will forgive us as well when we wrong Him (Matt. 6:12, 14-15).
Still taking this another step further, we are required to repay evil with good, as Jesus tells us not to resist an evil person (Matt. 5:38-42), but rather try to be perfect as God Himself by loving our enemies, blessing those who curse us, doing good to those who hate us, and praying for those who spitefully use us and persecute us (Matt. 5:43-48; 1 Peter 3:9).
As God’s children, instead of carrying out a personal vendetta against others who wrong us, we are required to live by Christ-honoring alternatives guided by the Holy Spirit. We should try our very best to live at peace with everyone (Rom. 12:18), submit to a spiritual mediator within the church (1 Cor. 6:1-6), and ultimately leave the ‘final justice’ to the hands of authorities who are ordained by God, and God Himself who is coming soon to “judge the world with righteousness and the peoples with His truth” (Psalm 96:10, 13).
Beloved, do not avenge yourselves, but rather give place to wrath; for it is written, "Vengeance is Mine, I will repay," says the Lord. Therefore "if your enemy is hungry, feed him; if he is thirsty, give him a drink; for in so doing you will heap coals of fire on his head." Do not be overcome by evil, but overcome evil with good. (Romans 12:19-21)