Astrophysics of dense quark matter in compact stars

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.