  Recent indications for high neutron star masses (M \sim 2 M_sun) and large
radii (R > 12 km) could rule out soft equations of state and have provoked a
debate whether the occurence of quark matter in compact stars can be excluded
as well. We show that modern quantum field theoretical approaches to quark
matter including color superconductivity and a vector meanfield allow a
microscopic description of hybrid stars which fulfill the new, strong
constraints. For these objects color superconductivity turns out to be an
essential ingredient for a successful description of the cooling phenomenology
in accordance with recently developed tests. We discuss the energy release in
the neutrino untrapping transition as a new aspect of the problem that hybrid
stars masquerade themselves as neutron stars. Quark matter searches in future
generations of low-temperature/high-density nucleus-nucleus collision
experiments such as low-energy RHIC and CBM @ FAIR might face the same problem
of an almost crossover behavior of the deconfinement transition. Therefore,
diagnostic tools shall be derived from effects of color superconductivity.
