  In this thesis, we report on results in non-anticommutative field theory and
twistor string theory, trying to be self-contained. We first review the
construction of non-anticommutative N=4 super Yang-Mills theory and discuss a
Drinfeld-twist which allows to regain a twisted supersymmetry in the
non-anticommutative setting. This symmetry then leads to twisted chiral rings
and supersymmetric Ward-Takahashi identities, which, when combined with the
usual naturalness argument by Seiberg, could yield non-renormalization theorems
for non-anticommutative field theories. The major part of this thesis consists
of a discussion of various geometric aspects of the Penrose-Ward transform. We
present in detail the case of N=4 super Yang-Mills theory and its self-dual
truncation. Furthermore, we study reductions of the supertwistor space to
exotic supermanifolds having even nilpotent dimensions as well as dimensional
reductions to mini-supertwistor and mini-superambitwistor spaces. Eventually,
we present two pairs of matrix models in the context of twistor string theory,
and find a relation between the ADHM- and Nahm-constructions and topological
D-brane configurations.
