  Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle
whose total space Z admits a natural metric h. The aim of this article is to
study properties of complex structures on (Z,h) which are compatible with the
CP1-fibration and the metric h. The results obtained enable us to translate
some metric properties on M in terms of complex properties on its twistor space
Z.
