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 give 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 an 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.