  Quasicrystals can be considered, from the point of view of their electronic
properties, as being intermediate between metals and insulators. For example,
experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have
conductivities far smaller than those of the metals that these alloys are
composed from. Wave functions in a quasicrystal are typically intermediate in
character between the extended states of a crystal and the exponentially
localized states in the insulating phase, and this is also reflected in the
energy spectrum and the density of states. In the theoretical studies we
consider in this review, the quasicrystals are described by a pure hopping
tight binding model on simple tilings. We focus on spectral properties, which
we compare with those of other complex systems, in particular, the Anderson
model of a disordered metal.
