God is so great that he sees every detail of our planet all the time. And God is so just that there is not a single injustice which doesn't infuriate him. So if he knows everything and hates all that's wrong, of course he "feels indignation everyday" (Psalm 7:11).
And this is not meant for terror — not if we treasure Jesus (Romans 5:9; 1 Thessalonians 1:10; 5:9). Rather, it's actually meant for our comfort. That's what Paul is getting at in Romans 12:19, "Beloved, never avenge yourselves, but leave it to the wrath of God, for it is written, 'Vengeance is mine, I will repay, says the Lord.'"
John Piper explains,
All of you have been wronged at one time or another. Most of you, probably, have been wronged seriously by someone who has never apologized or done anything sufficient to make it right. And one of the deep hindrances to your letting that hurt and bitterness go is the conviction — the justified conviction — that justice should be done, that the fabric of the universe will unravel if people can just get away with horrible wrongs and deceive everyone. That is one of the hindrances to forgiveness and letting grudges go. It’s not the only one. We have our own sin to deal with. But it is a real one. We feel that just to let it go would be to admit that justice simply won’t be done. And we can’t do it. So we hold on to anger, and play the story over and over again with the feelings: It shouldn’t have happened; it shouldn’t have happened; it was wrong; it was wrong. How can he be so happy now when I am so miserable? It is so wrong. It is so wrong!
This word in Romans 12:19 is given to you today by God to lift that burden from you. “Never avenge yourselves, but leave it to the wrath of God.” What does this mean for you? Laying down the burden of anger, laying down the practice of nursing your hurt with feelings of being wronged — laying that down — does not mean there was no great wrong against you. It does not mean there is no justice. It does not mean you will not be vindicated. It does not mean they just got away with it. No.
It means, when you lay down the burden of vengeance, God will pick it up.
This is not a subtle way of getting revenge. This is a way of giving vengeance to the one to whom it belongs. It is taking a deep breath, perhaps for the first time in decades, and feeling like now at last you may be free to love. I long so much for you to know the freedom to love.
Excerpted from Do Not Avenge Yourselves, But Give Place to Wrath, paragraphing and italics added.
For another helpful look at the wrath of God, see Tony's post: "The Avenger."