  Magnetic insulators in the regime of strong spin-orbit coupling exhibit
intriguing behaviors in external magnetic fields, reflecting the frustrated
nature of their effective interactions. We review the recent advances in
understanding the field responses of materials that are described by models
with strongly bond-dependent spin exchange interactions, such as Kitaev's
celebrated honeycomb model and its extensions. We discuss the field-induced
phases and the complex magnetization processes found in these theories and
compare with experimental results in the layered Mott insulators
$\alpha$-RuCl$_3$ and Na$_2$IrO$_3$, which are believed to realize this
fascinating physics.
