  The distinctive electronic properties of quasicrystals stem from their long
range structural order, with invariance under rotations and under discrete
scale change, but without translational invariance. This review introduces the
multiple manifestations of multifractality in the Fibonacci chain, a 1D
paradigm for quasicrystals. Quasiperiodic systems have been recently of
interest furthermore for their topological properties, described in this review
for the simplest 1D case. Some important generalizations of the basic
tight-binding models, and closely related models for other quasiperiodic
systems are also discussed.
