Humans as we know ourselves will cease to exist within a thousand years. Alternatively, humanity as we know it will be preserved indefinitely by our super-advanced descendants, but maintained the way we maintain populations of endangered animals in wildlife preserves.
I don’t know what will replace us, and maybe I really can’t know. Homo erectus really couldn't understand Homo sapiens when we swept across the globe and crushed them. The creatures that replace us might be biological, or they could be digital. Perhaps they’ll be neither, a new kind of life form invented by our superior biological or digital descendants.
The reason that our descendants (and replacements) are so hard to imagine or predict is that they will be the result of our newfound ability to self-program. Self-programming creates a positive feedback loop, and positive feedback loops spin out into overload. We’re going to see an “overload” of evolution, and it’s going to result in a life form that is beyond us.
Consider the genetic example. First, we learn how to manipulate genes to create or clone more intelligent humans. Then those humans use their superintelligence to develop better genetic science and create hypersuperiintelligent humans. Those humans reiterate until our descendants are unimaginably unlike us.
Consider the digital example. First, we learn how to create competent artificial intelligence. Then that artificial intelligence invents better artificial intelligence, which invents better AI, and there you have it again.
In either case, the superintelligent biological or digital intelligence that we create might in turn create some new sort of life that’s neither genetic nor digital (or both).
For that matter, our descendants are likely to diverge, especially as they take to the stars. So we’ll be replaced not by a new race but by some number of new races.
But then in the end everyone and everything will die when the universe collapses.
This rant informed by Fiasco, by Stanislaw Lem
Update: In Straw Dogs, John Gray points out that it's misleading to talk about "humankind" having a fate, as if there were a real entity called "humankind." There's just individuals, whose descendents will have quite different fates.