Over the last decade, the notion of global symmetry has undergone a broad and fruitful generalization. In this talk, I will discuss two striking applications of generalized symmetries: first, their role in constraining the low-energy dynamics of quantum many-body systems; and second, their utility in organizing and classifying the logical operations of quantum error-correcting codes. I will present a microscopic characterization of ’t Hooft anomalies associated with generalized symmetries in lattice models, and explain how these symmetries constrain dynamics through Lieb-Schultz-Mattis-type constraints. I will then describe how symmetry principles can be used to understand the logical operations of stabilizer codes, highlighting important examples such as the transversal T gate in two-dimensional non-Pauli codes realizing non-Abelian D4 topological order. This talk is intended as a broad summary of my work over the past few years, I will aim to emphasize the common conceptual thread connecting these developments.