The basic idea of deep learning has always seemed straightforward to me[0]. However, at least my perception is that it feels like there's a lot of deep magic going on in the details at the level that Google/Microsoft/Amazon/researchers are doing deep learning. That's honestly true of most active research areas[1], but since those results are also the results that keep getting a lot of attention, the "it's a black box" feeling makes sense to me. :)
[0] Having done both some moderately high level math and having a CS background, I feel like most ideas in CS fit this description, though. Our devil is the details.
[1] For instance: fairly recent results in weird applications of type theory are also super cool, and require some serious wizardry, but those get much less attention. (And are, I think, more taken for granted, since who doesn't understand a type system? /s)