  I review a number of recent developments in the physics of compact stars
containing deconfined quark matter, including (a)~their cooling with possible
phase transition from a fully gapped to a gapless phase of QCD at low
temperatures and large isospin, (b)~the transport coefficients of the 2SC phase
and the role played by the Aharonov-Bohm interactions between flux-tubes and
unpaired fermions; (c)~rapidly rotating compact stars and spin-down and spin-up
induced phase transition between hadronic and QCD matter as well as between
different phases of QCD.
