Holography appears to be a fundamental property of gravity. However, even in well-established models like AdS/CFT, the compatibility of this principle with the locality properties of the gravitational physics we observe remains to be completely understood. We can make progress in less than four spacetime dimensions by using special properties of the so-called T-Tbar operator in the CFT. I will discuss how the symmetries and preserved integrability structure provide an important handle on the properties of T-Tbar deformed CFTs. On the gravitational side, the relevant physics is that of the boundary modes of the metric, which implement the Brown--Henneaux charges. I will show how this reproduces the T-Tbar deformed field theory result and how similar techniques can be applied to asymptotically flat space to derive, among others, soft theorems for scattering amplitudes.
