Quasicrystals are ordered crystalline structures with no translational
symmetries. A quasicrystalline alloy was first observed by Shechtman in early
80's, for which he was awarded with the Nobel prize in Chemistry in 2011.

The mathematical characterization of quasicrystals is a challenging open
problem which attracted an increasing interest of researchers due to its
possible applications to several scientific fields, including photonic
computing.

We overview classical mathematical models for quasicrystals. A particular
attention will be given to one of the largest known class of mathematical
quasicrystals, the Meyer sets, and their relation with expansions in
non-integer bases.