  Experimental and theoretical aspects of Hall-type transport of spins in
magnetic insulators are reviewed, with emphasis on their spin chirality origin.
A general formalism for linear response theory of thermal Hall transport in the
spin model is developed, which can be applied to both the magnon and the
paramagnetic, spin-liquid regimes. Recent experiments on magnon-mediated
thermal Hall transport in the two-dimensional kagome, and three-dimensional
pyrochlore ferromagnetic insulators are reviewed in light of the multi-band
magnon theory of Hall transport, and compared to the more mysterious thermal
Hall transport found in the putative quantum spin ice material. As realizations
of spin-chirality driven magnon transport in the real space, we review the
general theory of emergent gauge fields governing the magnon dynamics in the
textured magnet, and discuss its application to the magnon-Skyrmion scattering
problem. Topological magnon Hall effect driven by the Skyrmion texture is
discussed.
