  Born-Infeld theory is the non-linear generalization of Maxwell
electrodynamics. It naturally arises as the low-energy effective action of open
strings, and it is also part of the world-volume effective action of D-branes.
The N=1 and N=2 supersymmetric generalizations of the Born-Infeld action are
closely related to partial spontaneous breaking of rigid extended
supersymmetry. We review some remarkable features of the Born-Infeld action and
outline its supersymmetric generalizations in four dimensions. The non-abelian
N=1 supersymmetric extension of the Born-Infeld theory and its N=1
supergravitational avatars are given in superspace.
