  Analytic and numerical results for quasiperiodic tight-binding models are
reviewed, with emphasis on two and three-dimensional models which so far are
beyond a mathematically rigorous treatment. In particular, we consider energy
spectra of aperiodic tight-binding models and the corresponding level
statistics, which are well reproduced by random matrix theory. The eigenstates
are characterised by multifractal analysis, and a construction of peculiar
multifractal states on the Penrose tiling is discussed. We also consider
quantum diffusion, and present some results on interacting electron systems in
one dimension.
