  We describe various approaches that give matrix descriptions of compactified
NS five-branes. As a result, we obtain matrix models for Yang-Mills theories
with sixteen supersymmetries in dimensions $2,3,4$ and 5. The equivalence of
the various approaches relates the Coulomb branch of certain gauge theories to
the moduli space of instantons on $T^4$. We also obtain an equivalence between
certain six-dimensional string theories. Further, we discuss how various
perturbative and non-perturbative features of these Yang-Mills theories appear
in their matrix formulations. The matrix model for four-dimensional Yang-Mills
is manifestly S-dual. In this case, we describe how electric fluxes, magnetic
fluxes and the interaction between vector particles are realized in the matrix
model.
