  Astrophysicists distinguish between three different types of compact stars.
These are white dwarfs, neutron stars, and black holes. The former contain
matter in one of the densest forms found in the Universe which, together with
the unprecedented progress in observational astronomy, make such stars superb
astrophysical laboratories for a broad range of most striking physical
phenomena. These range from nuclear processes on the stellar surface to
processes in electron degenerate matter at subnuclear densities to boson
condensates and the existence of new states of baryonic matter--like color
superconducting quark matter--at supernuclear densities. More than that,
according to the strange matter hypothesis strange quark matter could be more
stable than nuclear matter, in which case neutron stars should be largely
composed of pure quark matter possibly enveloped in thin nuclear crusts.
Another remarkable implication of the hypothesis is the possible existence of a
new class of white dwarfs. This article aims at giving an overview of all these
striking physical possibilities, with an emphasis on the astrophysical
phenomenology of strange quark matter. Possible observational signatures
associated with the theoretically proposed states of matter inside compact
stars are discussed as well. They will provide most valuable information about
the phase diagram of superdense nuclear matter at high baryon number density
but low temperature, which is not accessible to relativistic heavy ion
collision experiments.
