  This is the first article in the collection of reviews "Exact results on N=2
supersymmetric gauge theories", ed. J. Teschner. It describes how large
families of field theories with N=2 supersymmetry can be described by means of
Lagrangian formulations, or by compactification from the six-dimensional theory
with (2,0) supersymmetry on spaces of the form $M^4 \times C$, with C being a
Riemann surface. The class of theories that can be obtained in this way is
called class $\cal S$. This description allows us to relate key aspects of the
four-dimensional physics of class $\cal S$ theories to geometric structures on
C.
