  We survey results concerning reconfigurations of colourings and dominating
sets in graphs. The vertices of the $k$-colouring graph $\mathcal{C}_{k}(G)$ of
a graph $G$ correspond to the proper $k$-colourings of a graph $G$, with two
$k$-colourings being adjacent whenever they differ in the colour of exactly one
vertex. Similarly, the vertices of the $k$-edge-colouring graph
$\mathcal{EC}_{k}(G)$ of $g$ are the proper $k$-edge-colourings of $G$, where
two $k$-edge-colourings are adjacent if one can be obtained from the other by
switching two colours along an edge-Kempe chain, i.e., a maximal two-coloured
alternating path or cycle of edges.
  The vertices of the $k$-dominating graph $\mathcal{D}_{k}(G)$ are the (not
necessarily minimal) dominating sets of $G$ of cardinality $k$ or less, two
dominating sets being adjacent in $\mathcal{D}_{k}(G)$ if one can be obtained
from the other by adding or deleting one vertex. On the other hand, when we
restrict the dominating sets to be minimum dominating sets, for example, we
obtain different types of domination reconfiguration graphs, depending on
whether vertices are exchanged along edges or not.
  We consider these and related types of colouring and domination
reconfiguration graphs. Conjectures, questions and open problems are stated
within the relevant sections.
