The discovery, in 1984, of the first quasicrystalline alloy shown that
classical crystallography is not enough since is unable to incorporat
e structures with long-range non-periodic order. Further generalizatio
n is needed when we come to consider quasicrystals and other non-perio
dic structures in the same formalism. In this work, the current stage
of the crystallography of quasicrystals and the most successful atomic
models are reviewed. It will also emphasized the benefits that classi
cal crystallography has obtained since the discovery of quasicrystals.