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I will review advances for gravity in asymptotically flat spacetimes arising from investigations into their structure in the infrared. The recently-discovered infinite-dimensional symmetries of the scattering problem is the central result underlying much of the progress. Key examples include symmetry-based explanations for the previously-observed universal nature of infrared phenomena including soft theorems and memory effects. Moreover, the appearance of a Virasoro symmetry among the symmetries of four-dimensional gravity has led to a proposal for holography in which the scattering amplitudes in quantum gravity are dual to correlation functions of a two-dimensional conformal theory. The other infinite-dimensional symmetry groups place additional non-trivial constraints on the dual theory.