  This review presents recent breakthroughs in the realm of nonlinear Hall
effects, emphasizing central theoretical foundations and recent experimental
progress. We elucidate the quantum origin of the second-order Hall response,
focusing on the Berry curvature dipole, which may arise in inversion symmetry
broken systems. The theoretical framework also reveals the impact of disorder
scattering effects on the nonlinear response. We further discuss the
possibility of obtaining nonlinear Hall responses beyond the second order. We
examine symmetry-based indicators essential for the manifestation of nonlinear
Hall effects in time-reversal symmetric crystals, setting the stage for a
detailed exploration of theoretical models and candidate materials predicted to
exhibit sizable and tunable Berry curvature dipole. We summarize groundbreaking
experimental reports on measuring both intrinsic and extrinsic nonlinear Hall
effects across diverse material classes. Finally, we highlight some of the
other intriguing nonlinear effects, including nonlinear planar Hall, nonlinear
anomalous Hall, and nonlinear spin and valley Hall effects. We conclude with an
outlook on pivotal open questions and challenges, marking the trajectory of
this rapidly evolving field.
