  A vertex colouring of a graph $G$ is "nonrepetitive" if $G$ contains no path
for which the first half of the path is assigned the same sequence of colours
as the second half. Thue's famous theorem says that every path is
nonrepetitively 3-colourable. This paper surveys results about nonrepetitive
colourings of graphs. The goal is to give a unified and comprehensive
presentation of the major results and proof methods, as well as to highlight
numerous open problems.
