In this talk I will discuss aspects of global symmetry and their t Hooft anomalies in lattice systems. I will discuss how anomalies are defined and probed using topological defects, which will be applied to both internal and lattice symmetries. The latter arise in systems satisfying Lieb-Schultz-Mattis-type theorems. Using the example of a spin-1/2 XXZ chain, I will also discuss how the continuum limit of a lattice model is properly described in terms of a low-energy theory with topological defects. In particular, I will show that t Hooft anomaly explains a curious size dependence of the ground state lattice momentum in the spin-1/2 XXZ chain.