Decagonal quasicrystals – What has been achieved?

Where are we now, 25 years after the discovery of the first stable decagonal quasicrystal (DQC)? In this critical review, the status of research into these axial quasicrystals, which are quasiperiodic in two dimensions and periodic along the third, is discussed, and some of the open questions are addressed. We conclude that the structures of DQC are essentially known now, a few of them even as a function of temperature. Some hypotheses concerning DQC formation, growth and stability have still to be confirmed.