The self-dual Yang Mills equations are equations for a connection in a principal bundle on a 4-manifold with a real structure group such as SU(2). They have been a source of immeasurable geometric, analytic and topological interest since they were introduced to the mathematics community in the l960's. It is natural to define a complex connection with the same structure group; Kapustin and Witten have introduced a one parameter family of equations for this complexified connection which are related in a natural way to the Yang-Mills equations. We carefully review some of the geometry and topology of the self-dual Yang Mills connections and describe how the Kapustin-Witten equations are related to these older self-dual and anti self-dual equations. After touching briefly on interesting aspects of complex geometry which arise for these complex equations over a real four manifold, we finish by describing the basic unsolved question of the existence of global estimates.