This review is devoted to some aspects of non-linear Supersymmetry in four
dimensions that can be efficiently described via nilpotent superfields, in both
rigid and curved Superspace. Our focus is mainly on the partial breaking of
rigid N=2 Supersymmetry and on a class of generalized Born-Infeld systems
that originate from Special Geometry and on some prototype cosmological models,
starting from the Supergravity embedding of Starobinsky inflation. However, as
an aside we also review briefly some interesting two-field extensions of the
Born-Infeld Lagrangian whose field equations enjoy extended duality symmetries.Comment: Contribution to the Proceedings of "Group Theory, Probability, and
the Structure of Spacetime", A Conference on the Occasion of Professor V.S.
Varadarajan's Retirement, UCLA Mathematics Department, November 7-9, 2014. To
appear in a special issue of "p-Adic Numbers, Ultrametric Analysis and
Applications". 35 pages LaTeX, 1 eps figure. Typos corrected, reference adde
