Symmetries in Quantum Field Theory may have 't Hooft anomalies. If the symmetry is unbroken in the vacuum, the anomaly implies a nontrivial low-energy limit, such as gapless modes or a topological field theory. If the symmetry is spontaneously broken, for the continuous case, the anomaly implies low-energy theorems about certain couplings of the Goldstone modes. In the talk we will study the case of spontaneously broken discrete symmetries, such as Z/2 and T. Symmetry breaking leads to domain walls, and the physics of the domain walls is constrained by the anomaly. We will investigate how the physics of the domain walls leads to a matching of the original discrete anomaly. We will analyze the symmetry structure on the domain wall, which requires a careful analysis of some properties of the unbreakable CPT symmetry. We will demonstrate the general results on some examples and explain in detail the mod 4 periodic structure that arises in the Z/2 and T case. This gives a physical interpretation for the Smith isomorphism, which we will extend to more general abelian groups. We will show that via symmetry breaking and the analysis of the physics on the wall, the computations of certain discrete anomalies are greatly simplified.