It's murky concept though, so I wouldn't bet on mind uploading in our lifetime.
Some fairly fundamental things need to be answered first. Things like how does consciousness and the sense of self arise.
Naively, if you think that you are just a program that runs on a bunch of neurons in your brains, and that this program can be uploaded to a computer, you are still left with a very annoying problem: you upload a copy, and leave the original running in your squishy brain. So what then? Do you kill the original? But that involves killing a living and breathing human being. Do you wait until it dies naturally? That's still not a good answer, because you have to die so that a copy of you can continue existing.
So until we figure how to actually "teleport" our consciousness to some other host, we are in a pickle. And there's absolutely no evidence that we'll ever be able to do this teleportation. What if we never figure out the physics to do this?
Edit: I suppose you could sidestep this by generating fully digital consciousnesses that mimic what a human brain does. So a fully digital human. Assuming we can brute-force simulate a real human brain, this should be at least physically possible (as opposed to teleportation), but this still raises philosophical questions. What you are generating then aren't human beings, but conscious AI. You could argue that the human race would eventually be supplanted by immortal AI that are no longer bound by biology, but I'd argue that this isn't an evolution of the human race, rather a completely new life form (if you can call it that), which has nothing to do with humans except that we created it.