In order to extend the holographic principle to different signs of the cosmological constant beyond the standard AdS/CFT framework, the analysis of gravitational asymptotic symmetries proves to be a valuable tool. It allows for the exploration of various aspects of the dual CFT, as these symmetries correspond holographically to the global symmetries of the latter. Asymptotic symmetries differ from pure gauge symmetries in that they are associated with a nonzero conserved charge when one approaches the asymptotic boundary. However, in such a limit, the quantities defining these charges may diverge, necessitating their renormalization to assign them a well-defined physical meaning. While such a procedure is well understood for asymptotically AdS spacetimes, it remains far less clear in the case of asymptotically flat spaces. In this seminar, we will pedagogically review the holographic renormalization scheme in AdS and examine the current status in the flat background, aiming to identify key points that require further investigation to better understand the putative celestial/Carrollian dual CFT