In this talk, I will describe joint work with Langte Ma studying dimension reduction phenomena for absolute minimizers of the Yang-Mills functional. This work is motivated by special holonomy geometry and I will emphasize applications to gauge theory on special holonomy manifolds. I will explain the general approach to such phenomena that we develop, characterizing the moduli space of generalized anti-self-dual instantons on certain bundles over product Riemannian manifolds equipped with a parallel codimension-4 differential form. One outcome of this is an explicit description of instanton moduli spaces over certain product special holonomy manifolds.