  This is the second article in the collection of reviews "Exact results on N=2
supersymmetric gauge theories", ed. J. Teschner. The space of vacua of class
$\cal S$ theories on $R^3 \times S^1$ can be identified as the moduli space of
solutions to the self-duality equations in two dimensions on Riemann surfaces
studied by Hitchin. This fact plays a fundamental role for recent studies of
the spectrum of BPS states in class $\cal S$ theories, and it is related to the
integrable structure underlying Seiberg-Witten theory of theories of class
$\cal S$. This article reviews important aspects of the role of the Hitchin
system for the infrared physics of class $\cal S$ theories.
