  The Bondi-Metzner-Sachs-van der Burg (BMS) group is the asymptotic symmetry
group of radiating asymptotically flat spacetimes. It has recently received
renewed interest in the context of the flat holography and the infrared
structure of gravity. In this thesis, we investigate the consequences of
considering extensions of the BMS group in four dimensions with superrotations.
In particular, we apply the covariant phase space methods on a class of first
order gauge theories that includes the Cartan formulation of general relativity
and specify this analysis to gravity in asymptotically flat spacetime.
Furthermore, we renormalize the symplectic structure at null infinity to obtain
the generalized BMS charge algebra associated with smooth superrotations. We
then study the vacuum structure of the gravitational field, which allows us to
relate the so-called superboost transformations to the velocity kick/refraction
memory effect. Afterward, we propose a new set of boundary conditions in
asymptotically locally (A)dS spacetime that leads to a version of the BMS group
in the presence of a non-vanishing cosmological constant, called the
$\Lambda$-BMS asymptotic symmetry group. Using the holographic renormalization
procedure and a diffeomorphism between Bondi and Fefferman-Graham gauges, we
construct the phase space of $\Lambda$-BMS and show that it reduces to the one
of the generalized BMS group in the flat limit.
