  The Hall effects comprise one of the oldest but most vital fields in
condensed matter physics, and they persistently inspire new findings, such as
quantum Hall effects and topological phases of matter. The recently discovered
nonlinear Hall effect is a new member of the family of Hall effects. It is
characterized as a transverse Hall voltage in response to two longitudinal
currents in the Hall measurement, but it does not require time-reversal
symmetry to be broken. It has deep connections to symmetry and topology and,
thus, opens new avenues by which to probe the spectral, symmetry and
topological properties of emergent quantum materials and phases of matter. In
this Perspective, we present an overview of the recent progress regarding the
nonlinear Hall effect. We discuss the open problems, the prospects of the use
of the nonlinear Hall effect in spectroscopic and device applications, and
generalizations to other nonlinear transport effects.
