  In this chapter I focus on asking and answering the following questions: (1)
What is a black hole? Answer: There are three types of black holes, namely
mathematical black holes, physical black holes and astrophysical black holes.
An astrophysical black hole, with mass distributed within its event horizon but
not concentrated at the singularity point, is not a mathematical black hole.
(2) Can astrophysical black holes be formed in the physical universe? Answer:
Yes, at least this can be done with gravitational collapse. (3) How can we
prove that what we call astrophysical black holes are really black holes?
Answer: Finding direct evidence of event horizon is not the way to go. Instead
I propose five criteria which meet the highest standard for recognizing new
discoveries in experimental physics and observational astronomy. (4) Do we have
sufficient evidence to claim the existence of astrophysical black holes in the
physical universe? Answer: Yes, astrophysical black holes have been found at
least in some galactic binary systems, at the center of almost every galaxy,
and as the central engines of at least some long gamma-ray bursts. (5) Will all
matter in the universe eventually fall into black holes? Answer: Probably "no",
because "naked" compact objects, if they do exist with radii smaller than the
radii of event horizons for their masses but are not enclosed by event
horizons, can rescue the universe from an eternal death by re-cycling out the
matter previously accreted into astrophysical black holes. Finally I also
discuss briefly if we need a quantum theory of gravity in order to further
understand astrophysical black holes, and what further astronomical
observations and telescopes are needed to make further progress on our
understanding of astrophysical black holes.
