  Field theories on "quantum" or deformed space-time are considered here. The
Moyal-Weyl deformation breaks the Lorentz invariance of the theory, but one can
still require invariance under the supertranslation algebra. We investigate
some aspects of the Wess-Zumino model, super Yang-Mills theories and analyze
the correspondence of the later with the supersymmetric Born-Infeld action.
