Symmetry was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in the physics of the 21st century. As used today, there are a variety of interpretations of this term, which differ in meaning as well as their mathematical consequences. Symmetries of crystals, for example, generally express another kind of invariance than gauge symmetries, though in specific situations the distinctions may become quite subtle. I will review some of the various notions of symmetry and highlight some of their uses in specific examples taken from Pauli's scientific oevre.