  It was recently shown by Witten that B-type open topological string theory
with the supertwistor space CP^{3|4} as a target space is equivalent to
holomorphic Chern-Simons (hCS) theory on the same space. This hCS theory in
turn is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four
dimensions. We review the supertwistor description of self-dual and
anti-self-dual N-extended SYM theory as the integrability of super Yang-Mills
fields on complex (2|N)-dimensional superplanes and demonstrate the equivalence
of this description to Witten's formulation. The equivalence of the field
equations of hCS theory on an open subset of CP^{3|N} to the field equations of
self-dual N-extended SYM theory in four dimensions is made explicit.
Furthermore, we extend the picture to the full N=4 SYM theory and, by using the
known supertwistor description of this case, we show that the corresponding
constraint equations are (gauge) equivalent to the field equations of hCS
theory on a quadric in CP^{3|3}xCP^{3|3}.
