For more than a decade, quasicrystals were considered to exhibit only fundamental interest in so far that they have raised basic questions regarding the organization and stability of condensed matter. As well, they addressed the mechanisms of wave propagation in aperiodic solids. In more recent years, they turned to become useful materials in various mechanical devices, in solar absorbers or in heat insulation coatings. Nowadays, the science of quasicrystals, and especially the relevant high-dim crystallography techniques, have issued quite useful concepts and methods that prove useful in neighboring domains of condensed matter physics, of mechanics, of low temperature physics, etc. Hence, this article puts more emphasis on a few of the new subjects that quasicrystals science has helped us to study rather than on the few possible breakthroughs of quasicrystalline materials identified yet on the market.