  Classical black holes are solutions of the field equations of General
Relativity. Many astronomical observations suggest that black holes really
exist in nature. However, an unambiguous proof for their existence is still
lacking. Neither event horizon nor intrinsic curvature singularity have been
observed by means of astronomical techniques. This paper introduces to
particular features of black holes. Then, we give a synopsis on current
astronomical techniques to detect black holes. Further methods are outlined
that will become important in the near future. For the first time, the zoo of
black hole detection techniques is completely presented and classified into
kinematical, spectro-relativistic, accretive, eruptive, obscurative,
aberrative, temporal, and gravitational-wave induced verification methods.
Principal and technical obstacles avoid undoubtfully proving black hole
existence. We critically discuss alternatives to the black hole. However,
classical rotating Kerr black holes are still the best theoretical model to
explain astronomical observations.
