  This is a chapter in a forthcoming book on completely regular codes in
distance regular graphs. The chapter provides an overview, and some original
results, on codes in distance regular graphs which admit symmetries via a
permutation group acting on the vertices of the graph. The strongest notion of
completely transitive codes is developed, as well as the more general notion of
neighbour-transitive codes. The graphs considered are the Hamming, Johnson, and
Kneser graphs and their q-analogues, as well as some graphs related to
incidence structures.
