Deep-learned convolutional nets work wonders for visual recognition. Visual recognition via "the old AI" looked impossible by 1980, but today it looks easy.

(I see the visual segmentation models for self-driving cars from the "autonomous systems lab" in the next building over and think... It would be so easy to make something that honks for cyclists.)

Text analysis, reinforcement learning, etc. seem to be areas where deep learning might very well reach a plateau. In the case of images the meaning is not changed by a random "hot pixel", but changing one letter in a sentence can reverse the meaning of a sentence, changing one piece position in a chess game is the difference between a win or loss. These "binary" situations aren't a good match with the assumptions of continuity, differentiablity and such that neural networks depend on.