  It was recently argued that quantum field theories possess one-form and
higher-form symmetries, labelled `generalized global symmetries.' In this
paper, we describe how those higher-form symmetries can be understood
mathematically as special cases of more general 2-groups and higher groups, and
discuss examples of quantum field theories admitting actions of more general
higher groups than merely one-form and higher-form symmetries. We discuss
analogues of topological defects for some of these higher symmetry groups,
relating some of them to ordinary topological defects. We also discuss
topological defects in cases in which the moduli `space' (technically, a stack)
admits an action of a higher symmetry group. Finally, we outline a proposal for
how certain anomalies might potentially be understood as describing a
transmutation of an ordinary group symmetry of the classical theory into a
2-group or higher group symmetry of the quantum theory, which we link to WZW
models and bosonization.
