  This thesis is divided in two parts. The first part contains the study of
some properties of the electromagnetic duality in 4 dimensions. An extended
double potential formalism for linearized gravity is introduced which allows to
write an action manifestly invariant under duality rotations in presence of
both electric and magnetic external sources. It is also shown how, in the
reduced phase-space, all higher spin gauge fields can be written as
bi-hamiltonian systems. The role of the second hamiltonian is played by the
electromagnetic duality generator. The second part is devoted to the study of
asymptotic symmetries and their applications to holography. After a review of
symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we
apply a similar analysis to asymptotically flat spacetimes at null infinity in
3 and 4 dimensions. In particular, it is argued that the symmetry algebra of
asymptotically flat spacetimes at null infinity in 4 dimensions should be taken
as the semi-direct sum of supertranslations with infinitesimal local conformal
transformations and not, as usually done, with the Lorentz algebra. The first
applications are studied: an exact representation by bulk vector fields of the
asymptotic symmetry algebra through the introduction of a modified Lie bracket,
the derivation of how this symmetry algebra is realized on solution space and
the construction of the associated centrally extended surface charge algebra.
