I personally think Herbert could have ended his series here, as he manages to accomplish, with Leto Atreides II, all of the things he didn't manage with Paul. I'm going to reveal a ton of plot here, so bear with me. [Reading a review about what happens and reading the book are two different experiences, anyway, so you won't lose anything by reading what I type here.]
At the end of Children of Dune, Paul's son Leto II had merged with the "sandtrout" (larval form of the Dune sandworms) to become a super-human monster who was very close to invincible. It is speculated at the end of that book that he could live for 4,000 years. As God Emperor of Dune opens, it is 3,508 years after the events of Children, and Leto's sandtrout have transformed him into a human-sandworm hybrid, the only such animal in existence. Arrakis is now totally terraformed, and Leto has a tyrant's grip on the empire's dwindling supplies of the spice, melange.
Leto is a more powerful telepath than his father, and has the memories of all his ancestors--male and female--upon which to draw. He has become sensitive to moisture, and mostly lives in a citadel near the desert portion of Arrakis. Around him, the Bene Gesserit, the technologists of Ix, and the genetic manipulators of Bene Tleilax continue to weave their schemes in an effort to find his "secret stash" of spice.
The God Emperor has transformed society on an unprecedented level. Every world reflects the same pattern of life, and has been frozen by a ban on space travel. Only Leto's "Fish Speakers," an army composed entirely of women, are allowed free travel, and they perform the roles of conquerers and "civilizers." The clever part of forcing humanity into this pattern (which I didn't catch until I had read the book later) is that all of humanity gets to experience what age after age of peace is like. That was a big part of Herbert's story, after all: to show what life would be like for a person dependent upon prescience. And the verdict of that life is boredom.
Thrown into this mixture, of course, is a rebel Atreides, Siona, and the continually-reborn Duncan Idaho. They are considered crucial to Leto's breeding program for humanity. There is also a new, female ambassador from Ix, who allows Leto to recall his human side. All in all, there's a lot happening here, but Herbert manages to tell his story briskly. The usual quotes at the beginning of each chapter are usually excerpts from Leto's Journal, and provide (as usual) interesting comments about society and politics. I really enjoyed this book. To get a better, simpler look at Frank Herbert's universe, this serves as a triumphant example.