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Recently it has been observed that the string theory branes in geometric engineering and holography have a striking connection with generalized global symmetries. I will explain how branes, in a certain topological limit, not only furnish the symmetry generators, but also encode the so-called Symmetry Topological Field Theory (or SymTFT). For a d-dimensional quantum field theory (QFT), this is a (d+1)-dimensional topological field theory, whose topological defects encode both the symmetry generators (invertible or non-invertible) and the generalized charges. After having introduced the general setup, I will exemplify this for QFT with finite generalized (non-)invertible symmetries. Finally, I will extend this prescription to non-finite symmetries. In particular, I will discuss the symmetry theory (SymTh) for non-invertible symmetries with transformation parameters in Q/Z, which are the ones that also appear in 4d particle physics.