Never pay back evil for evil to anyone. Respect what is right in the sight of all men. If possible, so far as it depends on you, be at peace with all men. Never take your own revenge, beloved, but leave room for the wrath of God, for it is written, “Vengeance is Mine, I will repay,” says the Lord. “But if your enemy is hungry, feed him, and if he is thirsty, give him a drink; for in so doing you will heap burning coals on his head.” Do not be overcome by evil, but overcome evil with good. Romans 12:17-21 (NASB)
As a person begins to accept the pain of being a victim they can (and must) come to the place where by the power of the Holy Spirit they are able to forgive the offender.  In forgiving, the hurting heart turns over to God the responsibility for recompense. To be clear, this does not mean the hurt person offers forgiveness to the one who is unrepentant if they have not asked to be forgiven.  
What this means in daily life is the offended person must surrender their perceived right to revenge of any kind. This can be incredibly difficult, especially when the pain is enormous and raw and your heart may be broken by loss or betrayal of some kind.  But God makes it possible! In fact, it is not only possible to do; you can actually forgive with joy!
You may have been the victim of horrible people who have sought to take everything you value in life. Perhaps you have longed for revenge and went so far as to meditate on ways to retaliate against the person who hurt you. You have most likely realized that this kind of thinking fosters the anger you have in your heart and the more you think about how hurt you are the angrier you get!
While righteousness might be restraining you from ever acting out your thoughts of revenge against the person who hurt you; in your heart you commit murder daily.  I understand wanting revenge, wanting to strike back, wanting to inflict pain even though there may be no way you can ever repay enough evil for evil. I promise you, it will eat you up inside. You will become hateful in your heart and anger will be your constant companion.
When you determine to obey the conviction of the Holy Spirit there may be a mixture of relief and fear and discomfort. You will experience relief because in Christ there is a part of you that really does not want to live like that anymore. You will have a measure of fear that somehow you will not be avenged; that those who hurt you me will “get away with it.” You might have discomfort because and revisit feelings of abuse all over again for a short while.
When you begin to speak truth to yourself about what God says in the Word, and remind yourself that God is never late, and He is just and faithful to do what He says He will do it will become much easier to let it go and place it your hurt and anger and desire for revenge in His hands.
You must believe that one day God will avenge the wrong done to you. There is no sin that goes unpunished; there is always a price to be paid. What I am asking you to consider is that it is possible God has already exacted the penalty from the wrongdoer who sinned against you. It is possible He already has done so in Christ. It is possible that Christ has already paid the penalty for that sin their sin debt has been paid in full. It is possible that they have received grace and mercy and are now your sibling in Christ.
You have to remember that while you might believe they don’t deserve forgiveness, neither do you. While they don’t deserve mercy, neither do you! It is all of grace, and nothing else. The ground is level at the foot of the cross where all forgiven debtors stand, shoulder to shoulder praising our awesome and forgiving God.