  We review self-duality of nonlinear electrodynamics and its extension to
several Abelian gauge fields coupled to scalars. We then describe self-duality
in supersymmetric models, both N = 1 and N = 2. The self-duality equations,
which have to be satisfied by the action of any self-dual system, are found and
solutions are discussed. One important example is the Born-Infeld action. We
explain why the N = 2 supersymmetric actions proposed so far are not the
correct world-volume actions for D3 branes in d = 6.
