Appears in collection : Balzan Conference on Open Issues in Gravitation

A review of asymptotic symmetries of gravity in the asymptotically flat context will be given following the Hamiltonian (ADM) approach. General features (such as the form of the symmetry generators and the structure of the algebra) will be explained. The talk will also cover logarithmic supertranslations and explain how they lead to a remarkable simplification of the infinite-dimensional BMS algebra.