I will discuss our recent proposal for the Symmetry Topological Field Theory (SymTFT) for global, continuous spacetime symmetries ( https://arxiv.org/abs/2509.07965 ). For a d-dimensional theory, it is given by a (d + 1)-dimensional BF-theory for the
spacetime symmetry group, and whenever d is even, it includes also Chern-Simons couplings, that encode conformal and gravitational anomalies. This proposal is supported by the similarity to two-dimensional Jackiw-Teitelboim gravity in the d = 1 case and the topological limit of four-dimensional gravity in the d = 3 case. I will discuss how topological defects constructed from this SymTFT act by applying the associated spacetime symmetry transformation. Finally, I will discuss the relation to gravity and holography.