Psalm 78 is a historical psalm. It is similar to Psalms 105-106,
It tells the story of Israel's history much like Nehemiah 9; Ezekiel 16, 20, 23; and Acts 7.
It stresses the goodness of God to His people and His people's stubborn rebellion to Him.
It emphasizes both God's love and God's holiness and wrath and these attributes are seen against the picture of Israel's sin and rebellion.
78:1-8 The purpose of history
History teaches us not to forget God
History teaches us to put our trust in Him
History teaches us not to imitate bad examples

78:9-11 Ephraim's rebellion
 
78:12-16 God's goodness to Israel in Egypt and in the wilderness

78:17-20 The people continued to sin and rebel against God

78:21-33 God in His love provides for and in His wrath judges His people

78:34-39 God is gracious and compassionate and forgives the people

Jesus fulfills Psalm 78
78:2 He is a wisdom teacher greater than Solomon who speaks in parables- Matt. 13:34-35

78:19 He provides a table in the wilderness- Matt. 14:22-33; Mark 6:30-44; Luke 9:10-17; John 6:1-14

78:23-25 Jesus is the true bread from heaven- John 6:26-59