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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 coeffcients 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.