  Under extreme conditions of temperature and/or density, quarks and gluons are
expected to undergo a deconfinement phase transition. While this is an
ephemeral phenomenon at the ultra-relativistic heavy-ion collider (BNL-RHIC),
quark matter may exist naturally in the dense interior of neutron stars.
Herein, we present an appraisal of the possible phase structure of dense quark
matter inside neutron stars, and the likelihood of its existence given the
current status of neutron star observations. We conclude that quark matter
inside neutron stars cannot be dismissed as a possibility, although recent
observational evidence rules out most soft equations of state.
