In the last decade, the concept of symmetry in quantum systems has been significantly expanded to include so-called generalized symmetries, which can act on extended objects and need not be invertible. A central tool for their study is the Symmetry Topological Field Theory (SymTFT). After an introduction to these concepts, I will show how the SymTFT enables the systematic classification of quantum phases with generalized symmetries and the discovery of new examples with unexpected properties, such as degenerate vacua with different quantum entanglement. Finally, I will discuss how SymTFT ideas and techniques lead to new results in quantum computation.