  We discuss how one uses the thermodynamic formalism to produce metrics on
higher Teichm\"uller spaces. Our higher Teichm\"uller spaces will be spaces of
Anosov representations of a word-hyperbolic group into a semi-simple Lie group.
We begin by discussing our construction in the classical setting of the
Teichm\"uller space of a closed orientable surface of genus at least 2, then we
explain the construction for Hitchin components and finally we treat the
general case. This paper surveys results of Bridgeman-Canary-Labourie-Sambarino
"\emph{The pressure metric for Anosov representations}" and discusses questions
and open problems which arise.
