  15 years since its inception, Kitaev model still boasts only a narrow group
of material realizations. We review the progress in studying and understanding
one of them, lithium iridate Li$_2$IrO$_3$ available in three polymorphs that
host strong Kitaev interactions on spin lattices of different dimensionality
and topology. We also discuss feasibility, effectiveness, and repercussions of
tuning strategies based on the application of external pressure and chemical
substitutions.
