  The reversing symmetry group is a well-studied extension of the symmetry
group of a dynamical system, the latter being defined by the action of a single
homeomorphism on a topological space. While it is traditionally considered in
nonlinear dynamics, where the space is simple but the map is complicated, it
has an interesting counterpart in symbolic dynamics, where the map is simple
but the space is not. Moreover, there is an interesting extension to the case
of higher-dimensional shifts, where a similar concept can be introduced via the
centraliser and the normaliser of the acting group in the full automorphism
group of the shift space. We recall the basic notions and review some of the
known results, in a fairly informal manner, to give a first impression of the
phenomena that can show up in the extension from the centraliser to the
normaliser, with some emphasis on recent developments.
