Crystalline Color Superconductivity

We give an introduction crystalline color superconductivity, arguing that it is likely to occur wherever quark matter in which color-flavor locking does not occur is found. We survey the properties of this form of quark matter, and argue that its presence in a compact star may result in pulsar glitches, and thus in observable consequences. However, elucidation of this proposal requires an understanding of the crystal structure, which is not yet in hand.