  We analyze the phases of dense quark matter at nonzero quark masses. We map
out the phase diagrams for charged quark matter as well as charge neutral
matter containing leptons. We find that in Color Flavor Locked (CFL) quark
matter, the symmetric phase with equal numbers of $u$, $d$ and $s$ quarks is
unlikely to occur in nature. Various less symmetric phases with additional
meson condensates may play a role in neutron star cores, however, in agreement
with the analysis of Bedaque and Sch\"afer. We discuss the implications of
these novel color superconducting quark matter phases and their transitions for
neutron stars.
