  Massive neutron stars may harbor deconfined quark matter in their cores. I
review some recent work on the microphysics and the phenomenology of compact
stars with cores made of quark matter. This includes the equilibrium and
stability of non-rotating and rapidly rotating stars, gravitational radiation
from deformations in their quark cores, neutrino radiation and dichotomy of
fast and slow cooling, and pulsar radio-timing anomalies.
