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In this talk I will summarize some recent work on discrete symmetries in quantum gravity. If these symmetries are gauged they are sensitive to non-perturbative consistency constraints encoded in the associated anomalies. If these symmetries are not gauged, quantum gravity requires them to be broken and we want to explore the defects responsible for such a breaking of the symmetry. In both cases we learn about the universal features of the underlying theory, which we will discuss in some string theory (inspired) examples.