A conformally compact manifold is a complete Riemannian manifold with asymptotically negative curvature and with smooth compactification. We discuss the YangMills equations in this geometric context. It turns out that one can consider standard (i.e. smooth up to infinity) solutions, or solutions with a more complicated singularity (a Nahm pole) at infinity. We discuss a perturbative result in the standard case, along with a more complicated boundary value problem for singular instantons in dimension 4.