  The exactly solvable Kitaev model on the honeycomb lattice has recently
received enormous attention linked to the hope of achieving novel spin-liquid
states with fractionalized Majorana-like excitations. In this review, we
analyze the mechanism proposed by G. Jackeli and G. Khaliullin to identify
Kitaev materials based on spin-orbital dependent bond interactions and provide
a comprehensive overview of its implications in real materials. We set the
focus on experimental results and current theoretical understanding of planar
honeycomb systems (Na$_2$IrO$_3$, $\alpha$-Li$_2$IrO$_3$, and
$\alpha$-RuCl$_3$), three-dimensional Kitaev materials ($\beta$- and
$\gamma$-Li$_2$IrO$_3$), and other potential candidates, completing the review
with the list of open questions awaiting new insights.
