Psalms 78 and 79 are both attributed to Asaph. Both reflect the theology of the Deuteronomist: Israel's obedience brings blessing. Rebellions brings punishment.
Psalm 78 is lengthy but easily summarized. The Psalmist recounts Israel's history from the Exodus through the kingship of David. The purpose of this psalm is to teach the story of God and Israel to future generations. Israel's relationship with God is difficult.
Psalm 79 is a lament. Jerusalem has fallen. The temple has been desecrated. The psalmist interprets this as the signs of God's punishment. The psalmist cries out for revenge.
Next: Psalms 80-85