  Fifteen years since its inception, the 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.
