  We review current theoretical and experimental efforts to identify a novel
class of intermetallic 4f and 5f orbital materials in which strong interactions
between itinerant and predominately localized degrees of freedom gives rise to
a bulk insulating state at low temperatures, while the surface remains
metallic. This effect arises due to inversion of even parity conduction bands
and odd parity very narrow f-electron bands. The number of band inversions is
mainly determined by the crystal symmetry of a material and the corresponding
degeneracy of the hybridized f-electron bands. For odd number of band
inversions the metallic surface states are chiral and therefore remain robust
against disorder and time-reversal invariant perturbations. We discuss a number
of unresolved theoretical issues specific to topological Kondo insulators and
outline experimental challenges in probing the chiral surface states in these
materials.
