What does Psalm 137:9 mean?

This is among the most infamous verses in Scripture, and often badly misunderstood. God does not speak these words. The statement comes from a bitter and vengeful Israelite captive of Babylon (Psalm 137:1–3; 2 Chronicles 36:17–21). In his anger, the psalmist hopes Babylon will experience exactly what they did to the people of Israel (Psalm 137:8). Those atrocities (2 Kings 25:5–7) included the brutal slaughter of children, which was not unusual in ancient conquests (2 Kings 8:12; Isaiah 13:16; Hosea 10:14). This is a grieving cry that hopes a hated enemy will suffer the same evils they committed on others. Should that happen, the psalmist would justify and approve of the person who did it.

A graphic description of infant murder is perhaps the most gruesome imagery in the "imprecatory" psalms (Psalms 5; 10; 17; 35; 58—59; 69—70; 79; 83, 109; 129; 137; 140). These are prayers for the Lord to intervene in a specific, negative way against an enemy. Even here, however, the psalmist does not vow that he will "get even" with the Babylonians. Nor does he instruct anyone to carry out these acts. Instead, he openly bares his heart and places the results in God's hands. Scripture warns against taking revenge (Proverbs 19:11; Romans 12:19), but it does encourage prayers for the Lord's justice to be done (Psalm 7:6; Revelation 6:10). It also predicts that Babylon will experience what they have done to others (Jeremiah 25:14). Even in the imprecatory psalms, the emphasis is on the Lord's judgment and His action.