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We discuss two different approaches to integrability within the
framework of N=2 supersymmetric gauge theories. First we look at
theories with finite number of massive vacua and study their parameter
spaces. This approach leads to a description of quantum many-body
systems like spin chains. Second, moduli spaces of vacua of N=2 theories
can be conveniently described by VEVs of BPS line operators. In this
case the dual many-body system counterparts are models of Hitchin type
which arise as classical systems. In the talk I will explain how one can
relate integrable systems of the above two kinds and derive various
dualities between them.
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