  We review recent work on the study of N=2 super Yang-Mills theory with gauge
group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on
three main results: (i) We develop a new recursive method to compute the whole
instanton expansion of the low-energy effective prepotential; (ii) We interpret
the slow times of the hierarchy as additional couplings and promote them to
spurion superfields that softly break N=2 supersymmetry down to N=0 through
deformations associated to higher Casimir operators of the gauge group; (iii)
We show that the Seiberg-Witten-Whitham equations provide a set of non-trivial
constraints on the form of the strong coupling expansion in the vicinity of the
maximal singularities. We use them to check a proposal that we make for the
value of the off-diagonal couplings at those points of the moduli space.
