  Higher bundles are homotopy coherent generalisations of classical fibre
bundles. They appear in numerous contexts in geometry, topology and physics. In
particular, higher principal bundles provide the geometric framework for
higher-group gauge theories with higher-form gauge potentials and their
higher-dimensional holonomies. An $\infty$-categorical formulation of higher
bundles further allows one to identify these objects in contexts outside the
worlds of smooth manifolds or topological spaces. This article reviews the
theory of $\infty$-bundles, focussing on principal $\infty$-bundles, and
surveys several of their applications. It is an invited contribution to the
Topology section in the second edition of the Encyclopedia of Mathematical
Physics.
