In the last few years there has been a lot of interest in asymptotic symmetries in gauge theories and general relativity, in relation with deep infrared physics and memory effects. I will first give a brief pedagogical introduction showing how the surface charges associated with asymptotic symmetries follow from a standard application of Noether's theorem, and then discuss three extensions of the BMS symmetries that have been proposed in the context of general relativity, with their motivations. Among the new results, an algebraic perspective on the flux-balance laws of gravitational waves, a proposed modification of the Barnich-Troessaert bracket for the charges, and the possibility of discriminating bulk-equivalent descriptions of gravity such as metric and tetrad formulations, with some speculative implications for quantum gravity.
