Gapless phases of color-superconducting matter

We discuss gapless color superconductivity for neutral quark matter in beta equilibrium at zero as well as at nonzero temperature. Basic properties of gapless superconductors are reviewed. The current progress and the remaining problems in the understanding of the phase diagram of strange quark matter are discussed.Comment: 8 pages, 2 figures. Plenary talk at Strangeness in Quark Matter 2004 (SQM2004), Cape Town, South Africa, 15-20 September 2004. Minor correction