The properties and morphology of the cholesteric « blue » phase (BP) are discussed in terms of the « quasicrystalline » (QC) hypothesis, which states that the BP is ordered with three-dimensional translational periodicity. The lattice parameter of the « crystalline » BP is comparable to optical wavelengths, giving rise to Bragg diffraction effects. These effects provide the means by which the BP is made visible in reflection and transmission microscopy. Experimental evidence is presented which backs up this claim. A phase which may be the « liquid » version of the « crystalline » BP is reported for the first time. This phase looks like a uniform fog, with optical rotation in the same direction as the BP, and exists for some compounds in a narrow temperature range between the BP and isotropic state. Defects in the BP are shown, and found to be explainable as dislocations, further supporting the QC hypothesis. Linear arrays of such defects are found to occur, and to have the properties expected of low-angle grain boundaries. The phase transition seen by Bergmann et al. is discussed, with emphasis on the growth morphologies observed, and how it fits into the QC hypothesis.