  It is now known that when a massive star collapses under the force of its own
gravity, the final fate of such a continual gravitational collapse will be
either a black hole or a naked singularity under a wide variety of physically
reasonable circumstances within the framework of general theory of relativity.
The research of recent years has provided considerable clarity and insight on
stellar collapse, black holes and the nature and structure of spacetime
singularities. We discuss several of these developments here. There are also
important fundamental questions that remain unanswered on the final fate of
collapse of a massive matter cloud in gravitation theory, especially on naked
singularities which are hypothetical astrophysical objects and on the nature of
cosmic censorship hypothesis. These issues have key implications for our
understanding on black hole physics today, its astrophysical applications, and
for certain basic questions in cosmology and possible quantum theories of
gravity. We consider these issues here and summarize recent results and current
progress in these directions. The emerging astrophysical and observational
perspectives and implications are dicussed, with particular reference to the
properties of accretion discs around black holes and naked singularities, which
may provide characteristic signatures and could help distinguish these objects.
