Ever hear someone utter this phrase? Usually not a happy moment, is it? It's usually a time where someone (maybe you) has been wronged and is vowing that this act will NOT be forgotten and WILL be avenged.
In the movie The Princess Bride there is a character named Inigo Montoya who spends the entire movie (and as we learn the whole of his life) chasing a six-fingered man who killed his father. He tells the hero near the beginning of the movie is, "When I meet that man I will say, 'Hello, my name is Inigo Montoya. You killed my father. Prepare to die.'" Eventually he does end up meeting the six-fingered man and taking his revenge, so that at he end of the movie he says, "I have been in the revenge business so long, now it's over, I don't know what to do with the rest of my life."
In Psalm 10 we see David wondering why the Lord stands "so far away" hiding in times of trouble. Wicked men have pursued David and he longs to see them getting their just desserts. David sees all that the wicked do to the oppressed and helpless, but David does not plot revenge.
When David was pursued by King Saul, he had opportunities to kill Saul and take his revenge on him and have the throne, but David knew this was not God's way. He told his men that when God wanted him on the throne God would be the one to make it happen. David should not force it.
Here in Psalm 10, David is saying the same thing. While the "wicked person despises God" and says to himself that God "will not demand an account", David reminds himself and us that God does see the trouble and grief brought on by these oppressors. God is our helper, and He is the one who will take care of the wicked and oppressor. He will do "justice for the fatherless and oppressed." Not only that, David says He will strengthen the heart of the oppressed.
So do not waste your life in the pursuit of revenge. Instead do as Paul says,
"Do not repay anyone evil for evil. Try to do what is honorable in everyone's eyes. If possible, on your part, live at peace with everyone. Friends, do not avenge yourselves; instead leave room for His wrath. For it is written: Vengeance belongs to Me; I will repay, says the Lord. But if your enemy is hungry, feed him. If he is thirsty, give him something to drink. For in so doing you will be heaping fiery coals on his head. Do not be conquered by evil, but conquer evil with good." (Psalm 12:17-21)
A far better pursuit, and one you won't regret later.