  We review here some of the major open issues and challenges in black hole
physics today, and the current progress on the same. It is pointed out that to
secure a concrete foundation for the basic theory as well as astrophysical
applications for black hole physics, it is essential to gain a suitable insight
into these questions. In particular, we discuss the recent results
investigating the final fate of a massive star within the framework of the
Einstein gravity, and the stability and genericity aspects of the gravitational
collapse outcomes in terms of black holes and naked singularities. Recent
developments such as spinning up a black hole by throwing matter into it, and
physical effects near naked singularities are considered. It is pointed out
that some of the new results obtained in recent years in the theory of
gravitational collapse imply interesting possibilities and understanding for
the theoretical advances in gravity as well as towards new astrophysical
applications.
