In science, if something isn't directly observable it can't be "discovered." There is only indirect evidence of black holes. The existence of black holes has been a topic of speculation for hundreds of years, but John Wheeler is credited with coining the term, "black hole," in 1969.
The two kinds of black holes are those amongst solar masses caused by supernovae and the larger variety at the center of galaxies. Einstein predicted the existence of black holes in his general theory of relativity, published in 1916. In 1971, Cygnus X-1, an X-ray binary star, became the first object to be recognized as a black hole.