  Two-dimensional electron gases in strong magnetic fields provide a canonical
platform for realizing a variety of electronic ordering phenomena. Here we
review the physics of one intriguing class of interaction-driven quantum Hall
states: quantum Hall valley nematics. These phases of matter emerge when the
formation of a topologically insulating quantum Hall state is accompanied by
the spontaneous breaking of a point-group symmetry that combines a spatial
rotation with a permutation of valley indices. The resulting orientational
order is particularly sensitive to quenched disorder, while quantum Hall
physics links charge conduction to topological defects. We discuss how these
combine to yield a rich phase structure, and their implications for transport
and spectroscopy measurements. In parallel, we discuss relevant experimental
systems. We close with an outlook on future directions.
