This psalm speaks of an ideal king

72:1-4, 12-14 The king does justice and righteousness.
He cares for the weakest and most defenseless.

72:8-11 His reign is universal

72:5-7, 15-17 Prosperity and blessing will be in his time and the people bless him that his reign will be forever

72:18=20. A doxology closes this second book of the Psalms.
Book 1- Psalms 1-41
Book 2- Psalms 42-72
Book 3- Psalms 73-89
Book 4- Psalms 90-106
Book 5- Psalms 107-150

David (II Sam. 8:15-18); Solomon (I Kings 10:9); and Josiah (Jer. 22:15-16) were said to do justice and righteousness. But none of them lived up to all that was in the psalm. 

The last king of Judah was captured, his sons were killed before him, and then his eyes were put out. What about the universal reign of 72:8-11?
The Jewish people continued to keep this psalm and to read it and it inspired hope of a king who would come. It gave them hope of a Messiah.

Jesus is the ultimate fulfillment of this king above all kings.