ABSTRACT
This chapter deals with some new global results in twistor geometry. It describes a basic problem in complex geometry and presents a theorem to establish a sort of dictionary between conformal properties and complex properties of twistor space. There is another circle of ideas one can imagine behind the twistor geometry: the so called generalized Kaluza-Klein theories, i.e., roughly speaking, how to encode the physics of the universe into the geometry of a principal bundle.
