Dearly beloved, avenge not yourselves, but rather give place unto wrath: for it is written, Vengeance is mine; I will repay, saith the Lord.
- Romans 12:19 (KJV)
Vengeance is not for us. It's far too easy for us to become consumed with these kind of powerful feelings. God tells us to step aside, and make room for His wrath.
Breaking God's Law comes with a penalty. Most people understand this from our own judicial system, e.g. you break the law, you pay the fine/punishment, etc.
Vengeance can sometimes be hard to understand, e.g. why not just stop someone's life force instead? But is this fair? For example, let's say someone has committed hideous crimes - killing people even. Should that person then be sentenced to death without some kind of punishment? Is that fair to his victims? No, of course not.
God is righteous, and promises justice.
For we must all appear before the judgment seat of Christ; that every one may receive the things done in his body, according to that he hath done, whether it be good or bad.
- 2 Corinthians 5:10 (KJV)
As Children of God we have nothing to fear from God.
The wicked on the other hand:
It is a fearful thing to fall into the hands of the living God.
- Hebrews 10:31 (KJV)
These are the end times, and God has put on His armor (which includes vengeance):
For he put on righteousness as a breastplate, and an helmet of salvation upon his head; and he put on the garments of vengeance for clothing, and was clad with zeal as a cloak.
- Isaiah 59:17 (KJV)
There is still time to repent, but time is running out!!