  We discuss recent progress in the understanding of the vacuum structure
(effective superpotentials) of confining gauge theories with N=1 supersymmetry.
Even for non-supersymmetric theories, appropriate perturbative calculations
(e.g. using the background field method) give non-perturbative information
about the vacuum structure. However, in supersymmetric theories, these results
are often exact.
  The gauge theory effective superpotential is encoded by a hyperelliptic
curve, which emerges from the geometry of the string theory background, and may
be rederived using other techniques based on zero-dimensional matrix integrals,
the dynamics of integrable systems and the factorization of Seiberg-Witten
curves. We describe in detail how each technique highlights complementary
aspects of the gauge theory.
  The spectral curve requires the introduction of additional fundamental matter
fields, which act as UV regulators by embedding the gauge theory in a UV-finite
theory. We focus in detail on maximally-confining vacua of N=1 gauge theories
with fundamental matter, and of theories with SO and Sp gauge groups. Both
cases require refinements to the basic techniques used for SU gauge theory
without fundamental matter.
  We derive explicit general formulae for the effective superpotentials of N=1
theories with fundamental matter and arbitrary tree-level superpotential, which
reproduce known results in special cases. The problem of factorizing the
Seiberg-Witten curve for N=2 gauge theories with fundamental matter is also
solved and used to rederive the corresponding N=1 effective superpotential.
