Psalm 37 is a wisdom song. Its message is: trust in the Lord to take care of things and be content. The writer acknowledges that evildoers success on earth. But we are not to fret over them. We are to trust God to dispense justice in his own time. We are to trust him. We reflect our trust in our trusting actions. We are to do good, be faithful, delight in the Lord, commit our way to him, be still before him, wait patiently for him, refrain from anger, and again, do not fret. In other words, let God take care of the bad folks and trust him to be just while you reflect God's gracious character in the way you treat people and in your attitude toward life.
The promise in Psalms is that the meek, those who live in trusting obedience to God, will inherit the land. For Jews that meant living in peace in the allotment they were given in Israel. Note, though, that Jesus expanded the promise. He said "the meek will inherit the earth". (Matthew 5:6) Those who trust in God through faith in Jesus will inherit the whole earth. Revelation completes the picture for us, showing us a restored earth with a beautiful new city where the redeemed will live in the presence of the Lord forever.
Don't worry. Trust. Live graciously.