  For ${\cal N}=2^*$ theory with $U(N)$ gauge group we evaluate expectation
values of Wilson loops in representations described by a rectangular Young
tableau with $n$ rows and $k$ columns. The evaluation reduces to a two-matrix
model and we explain, using a combination of numerical and analytical
techniques, the general properties of the eigenvalue distributions in various
regimes of parameters $(N,\lambda,n,k)$ where $\lambda$ is the 't Hooft
coupling. In the large $N$ limit we present analytic results for the leading
and sub-leading contributions. In the particular cases of only one row or one
column we reproduce previously known results for the totally symmetry and
totally antisymmetric representations. We also extensively discusss the ${\cal
N}=4$ limit of the ${\cal N}=2^*$ theory. While establishing these connections
we clarify aspects of various orders of limits and how to relax them; we also
find it useful to explicitly address details of the genus expansion. As a
result, for the totally symmetric Wilson loop we find new contributions that
improve the comparison with the dual holographic computation at one loop order
in the appropriate regime.
