I don't think computers will be able to pass the Turing test and have conversations in which they are indistinguishable from humans.
I don't think that we'll make a program that can display a generalized understanding of the world. Yes, can play go, but doesn't know what go pieces are. I don't think "deep learning" will solve this. At some point the program will trip up and make it easy to spot that it doesn't understand what it is doing.
Anything that requires the program to "genuinely understand" something I think will beyond the reach of computers. We will gradually understand better ourselves where that distinction is. For instance, it used to be thought that the game of Go required genuine understanding, even for amateur level - but apparently not.
For background about why I think this, see Why Strong Artificial Intelligences Need Protection From Us - Not Us From Them