Abstract: A myriad of generalisations and extensions of the BMS3 algebra have seen a surge in interest in the recent years due to their relations to various areas of physics, such as flat-space holography, tensionless strings, ambitwistor strings, soft-theorems, AdS3 gravity etc. In this talk, the construction of the BRST complexes of these algebras resulting from studying their semi-infinite cohomology using VOA techniques is discussed. Some embedding theorems and their formulation in terms of twisted N=2 SCFTs are also presented, along with a few preliminary implications of our findings to special cases of these algebras that are of interest. Based on joint work with José Figueroa-O'Farrill, and some ongoing work with Joaquim Gomis, Carles Batlle and Victor Campello.