  Different string theories in twistor space have recently been proposed for
describing ${\cal N}=4$ super-Yang-Mills. In this paper, my Strings 2003 talk
is reviewed in which a string theory in $(x,\theta)$ space was constructed for
self-dual ${\cal N}=4$ super-Yang-Mills. It is hoped that these results will be
useful for understanding the twistor-string proposals and their possible
relation with the pure spinor formalism of the $d=10$ superstring.
