First off, this is the wrong question. (It's a good example, by the way, of how important getting the right question is to a good discussion.) The right question is: What is your image of what life is going to be like just before, during and after "The Singularity"? I will define Singularity shortly.
When we plan for most things we use linear extrapolation. Example: "I just got a new job that pays a bundle. Yay! If I save $1000 a month how much will I have at the end of the year?" The linear extrapolation answer is $12,000. But if I say instead, "If each month I put that $1000 into an investment account earning 10% a year." then the answer will be different because there is exponential growth involved.
Asking what will happen in 100, 200, 500 years is asking for linear extrapolation, but human knowledge and prosperity are growing exponentially. And if you don't scare yourself with the kind of "sky is falling"-type worries that power post-apocalypse stories, we don't yet see a limit to those increases. So the different question must be asked: The Singularity question I posed above.
The Singularity is a concept that has been around a while and popularized these days by Ray Kurzweil and his book The Singularity is Near. The basic idea is that the combination of growing computing power, bioengineering and nanotechnology is going to change things so quickly in the near future that living on Earth will become unrecognizable to mere human mortals. Further, this "flip", the Singularity, is likely to happen sometime in the 21st century -- almost time to Hold your Breath!
I predict a variant on that theme. I predict that higher intelligences will be created, several times and in several ways, but there will still be humans on Earth, and they will still face human problems, the kind we can recognize today. The higher intelligences will come to exist. They will be real. But they will do things and worry about things that humans can't comprehend, so they will have little impact on human living. We will take them for granted. Think of the relation between humans and the bacteria we evolved from: +99% of bacteria on Earth today don't have a clue that humans exist, and those few that do interact with us don't have a clue what we are up to. They just can't comprehend us, but we both co-exist quite happily on Earth. (I have written about this kind of relation in my essay "The Cow-Human Relation, from the Cow Perspective" in my book Science and Insight for Science Fiction Writing.) We will have that relation with the post-Singularity intelligences that spring from human technologies and inventiveness.
Those entities will be writing their own history. For us they will be unthinkable -- we will not be able to wrap our heads around what they are or what they do. (I write about some of these entities being created in my story "The Failure" in Tips for Tailoring Spacetime Fabric Vol. 2.) But we humans will still be around and we will still have plenty of human-oriented day-to-day living to think about. That's what I'm writing about in Child Champs. We humans will experience things such as driverless cars and Avatar Cruise Ships -- cruise ships that sail around from port to port, but don't have a single person on board -- they just carry avatars. Why? They are a lot cheaper and safer and even more fun!