Neutron stars have long been regarded as extra-terrestrial laboratories from
which we can learn about extreme energy density matter at low temperatures. In
this article, I highlight some of the recent advances made in astrophysical
observations and related theory. Although the focus is on the much needed
information on masses and radii of several individual neutron stars, the need
for additional knowledge about the many facets of neutron stars is stressed.
The extent to which quark matter can be present in neutron stars is summarized
with emphasis on the requirement of non-perturbative treatments. Some
longstanding and new questions, answers to which will advance our current
status of knowledge, are posed.Comment: 18 pages, 3 figures, 3 tables, Review submitted to Praman
