Shazam is the closest thing we have to witchcraft. I'm sure plenty of HNers will chime in with "well acktually..." type comments about how they could write it in their basement in a weekend, but to do what it does, as quickly as it does, on the ridiculously enormous library of music that it does is really something special.
The remaining thing I don't understand now is how the heck they managed to negotiate the license for all the songs they have in the database. A friend of mine had a major website for lyrics, and he got some legal trouble from the record companies. When he tried to buy a license to display the lyrics, after some back and forth, they basically said they're not interested in licensing. This was in the early 2000s before streaming took off. Since that time I have the impression that often legal and social problems are much harder to solve than technological ones.