  In the last 30 years, the mathematical theory of aperiodic order has
developed enormously. Many new tilings and properties have been discovered, few
of which are covered or anticipated by the early papers and books. Here, we
start from the well-known Fibonacci chain to explain some of them, with
pointers to various generalisations as well as to higher-dimensional phenomena
and results. This should give some entry points to the modern literature on the
subject.
