  There has been a recent surge of interest in using light and sound as
platforms for studying non-Abelian physics. Through a kaleidoscope of physical
effects, light and sound provide diverse ways to manipulate their degrees of
freedom to constitute the Hilbert space for demonstrating non-Abelian
phenomena. The review aims to provide a timely and comprehensive account of
this emerging topic. Starting from the foundation of matrix-valued geometric
phases, we cover non-Abelian topological charges, non-Abelian gauge fields,
non-Abelian braiding, non-Hermitian non-Abelian phenomena, and their
realizations with photonics and acoustics. This topic is fast evolving at the
intersection of atomic, molecular, optical physics, condensed matter physics,
and mathematical physics, with fascinating prospects ahead.
