The 2011 Nobel Prize in chemistry has been awarded to Dan Shechtman for his discovery of quasicrystals. The discovery has indeed been a breakthrough in crystallography and solid state physics and chemistry. After a brief introduction to the subject, we review some of the recent advances in the understanding of the atomic structure of icosahedral quasicrystals and in particular for the binary Cd-Yb type quasicrystal. Thanks to a combined analysis of periodic approximant, high quality synchrotron data, and the superspace approach, a detailed insight in the crystal chemistry of this binary quasicrystal has been achieved.