A generalised $n$-gon is an incidence structure whose bipartite
incidence graph has diameter $n$ and girth $2n$. Many of the known
examples are highly symmetric, and in fact
arise naturally from particular group actions.
I will give an overview of some things that are known about
symmetries of generalised $n$-gons, leading toward
classification of these objects, or at least to understanding the
symmetry they can have. My contributions to this problem are
based on joint work with John Bamberg, Michael Giudici and Gordon Royle of the University of Western Australia,
and Pablo Spiga of the University of Milan.