  Investigations of deconfined quark matter within NJL-type models are
reviewed, focusing on the regime of low temperatures and ``moderate''
densities, which is not accessible by perturbative QCD. Central issue is the
interplay between chiral symmetry restoration and the formation of color
superconducting phases. In order to lay a solid ground for this analysis, we
begin with a rather detailed discussion of two and three-flavor NJL models and
their phase structure, neglecting the possibility of diquark pairing in a first
step. An important aspect of this part is a comparison with the MIT bag model.
The NJL model is also applied to investigate the possibility of absolutely
stable strange quark matter. In the next step the formalism is extended to
include diquark condensates. We discuss the role and mutual influence of
several conventional and less conventional quark-antiquark and diquark
condensates. As a particularly interesting example, we analyze a spin-1 diquark
condensate as a possible pairing channel for those quarks which are left over
from the standard spin-0 condensate. For three-flavor systems, we find that a
self-consistent calculation of the strange quark mass, together with the
diquark condensates, is crucial for a realistic description of the 2SC-CFL
phase transition. We also study the effect of neutrality constraints which are
of relevance for compact stars. Both, homogeneous and mixed, neutral phases are
constructed. Although neutrality constraints generally tend to disfavor the 2SC
phase we find that this phase is again stabilized by the large values of the
dynamical strange quark mass which follow from the self-consistent treatment.
Finally, we combine our solutions with existing hadronic equations of state to
investigate the existence of quark matter cores in neutron stars.
