  We study matrix models in the beta ensemble by building on the refined
recursion relation proposed by Chekhov and Eynard. We present explicit results
for the first beta-deformed corrections in the one-cut and the two-cut cases,
as well as two applications to supersymmetric gauge theories: the calculation
of superpotentials in N=1 gauge theories, and the calculation of vevs of
surface operators in superconformal N=2 theories and their Liouville duals.
Finally, we study the beta deformation of the Chern-Simons matrix model. Our
results indicate that this model does not provide an appropriate description of
the Omega-deformed topological string on the resolved conifold, and therefore
that the beta-deformation might provide a different generalization of
topological string theory in toric Calabi-Yau backgrounds.
