  In this thesis we take Einstein theory in dimension four seriously, and
explore the special aspects of gravity in this number of dimension. Among the
many surprising features in dimension four, one of them is the possibility of
`Chiral formulations of gravity' - they are surprising as they typically do not
rely on a metric. Another is the existence of the Twistor correspondence. The
Chiral and Twistor formulations might seems different in nature. In the first
part of this thesis we demonstrate that they are in fact closely related. In
particular we give a new proof for Penrose's `non-linear graviton theorem' that
relies on the geometry of SU(2)-connections only (rather than on metric). In
the second part of this thesis we describe partial results towards encoding the
full GR in the total space of some fibre bundle over space-time. We indeed show
that gravity theory in three and four dimensions can be related to theories of
a completely different nature in six and seven dimension respectively. This
theories, first advertised by Hitchin, are diffeomorphism invariant theories of
differential three-forms. Starting with seven dimensions, we are only partially
succesfull: the resulting theory is some deformed version of gravity. We
however found that solutions to a particular gravity theory in four dimension
have a seven dimensional interpretation as G2 holonomy manifold. On the other
hand by going from six to three dimension we do recover three dimensional
gravity. As a bonus, we describe new diffeomorphism invariant functionnals for
differential forms in six dimension and prove that two of them are topological.
