  We review recent results on symmetries of asymptotically flat spacetimes at
null infinity. In higher dimensions, the symmetry algebra realizes the
Poincar\'e algebra. In three and four dimensions, besides the infinitesimal
supertranslations that have been known since the sixties, the algebras are
evenly balanced because there are also infinitesimal superrotations. We provide
the classification of central extensions of the bms3 and bms4 algebras.
Applications and consequences as well as directions for future work are briefly
indicated.
