First of all, do black holes exist?
Yes, they do! (However, it is true that there are still some mysteries concerning black holes. Some of them are related to the origin of the universe! Solving these problems may expand our knowledge about the Big Bang towards its first instants, the Planck time, but that’s another “story”.)
(If you prefer to read this article in Portuguese: Buracos Negros.)
A brief definition:
Sophia of Nature 