  We review Mirzakhani's recursion for the volumes of moduli spaces of
orientable surfaces, using a perspective that generalizes to non-orientable
surfaces. The non-orientable version leads to divergences when the recursion is
iterated, from regions in moduli space with small crosscaps. However, the
integral kernels of the recursion are well-defined and they map precisely onto
the loop equations for a matrix integral with orthogonal symmetry class and
classical density of eigenvalues proportional to $\sinh(2\pi\sqrt{E})$ for
$E>0$. The recursion can be used to compute regularized volumes with a cutoff
on the minimal size of a crosscap.
