I'm gonna talk about which direction Computer Science is heading to, specifically on technical aspect, not applications.
We have to begin with some philosophy. The most eager question is, what is computers and what can it do? In fact, computers are just a bunch of electric circuits. Some are for converting physical information into electrical signals of 1's and 0's or reverse , e.g. gyroscope, light sensor, graphic processor, etc. The rest of those circuits are for only one thing: logical simulation. Some call it computation, but logical simulation is what I prefer. Think about it for a while: everything happens in computers is not real, but a bunch of electrical signals. Of course, this doesn't mean computers have no impact on real life. My point is, we can take computers as machines which can simulate (almost) all kinds of logic abstractions of phenomenons. Thus computer can do anything that we can abstract to logic.
The road of computer evolution is all the way along which of human understanding. The computers do things in the way we think things should be done. This doesn't have to imply computers can't surpass human beings.
The current stage is computational simulation. We give specific instructions of steps on particular operating objects. The next stage is gonna be Artificial Intelligence. We don't get in too deep, just give them the capability of thinking and let them do on their own. I'm very excited to meet it one day. Just prey it won't be like The Matrix. So, let's get back on track: where does it end up with computers?
AI is not everything. It's just a simulation of human reasoning. I don't think it's the ultimate goal of logical simulation. There're many others areas we need computers' help. There're edges for computer's capability (No need to mention Turing problem), and also for human understanding.
I think, computer evolution ends where human understanding reaches limits. But this definitely doesn't mean computers are in the same bounds with humans. And hopefully maybe one day, they can tell us what's happened before time began.