  For the past 20 years it had been thought that the coexistence phase of the
confined hadronic and quark matter phases, assumed to be a first order
transition, was strictly excluded from neutron stars. This, however, was due to
a seemingly innocuous idealization which has approximated away important
physics. The reason is that neutron stars constitute multi-component bodies
rather than single-component ones formerly (and incorrectly) used to describe
the deconfinement phase transition in neutron stars. So, contrary to earlier
claims, `neutron' stars may very well contain quark matter in their cores
surrounded by a mixed-phase region of quark and hadronic matter. Such objects
are called hybrid stars. The structure of such stars as well as an observable
signature that could signal the existence of quark matter in their cores are
discussed in this paper.
