  There exist many four dimensional integrable theories. They include self-dual
gauge and gravity theories, all their extended supersymmetric generalisations,
as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the
harmonic space formulation of the twistor transform for these theories which
yields a method of producing explicit connections and metrics. This formulation
uses the concept of harmonic space analyticity which is closely related to that
of quaternionic analyticity. (Talk by V. Ogievetsky at the G\"ursey Memorial
Conference I, Istanbul, June 1994)
