Categorical groups formalize situations, where the symmetries of an object are themselves related by symmetries. Their relevance to string theory has been known for a while, and their theory is developing rapidly. We will attempt to fill the theory with life by discussing examples, ranging from the symmetries of the platonic solids with some extra structure to the Schur extensions of the alternating groups, which turn out to be closely linked to the stable three stem, to categorical extensions of sporadic groups and of Lie groups.