  We review the cubic rare-earth boride series which displays diverse
electronic states like localized 4f electron multiplets split by the crystal
electric field (CEF), itinerant heavy-fermion quasiparticle bands of the Kondo
lattice as well as gapped Kondo insulator or mixed-valent semiconductor states.
Fairly exotic states may appear due to the 'hidden' order of multipoles carried
by degenerate CEF multiplets, in addition to magnetic order present in many RB6
(R = rare earth) compounds. Most prominent are CeB6 and its La-diluted alloys
which exhibit antiferro-quadrupolar and octupolar ordering enabled by the cubic
G8 quartet state. The associated collective excitations are multipolar waves
with a dispersion characteristic for the underlying order and accessible by
inelastic neutron scattering. This localized multipolar-moment picture of
R-borides is complemented by the itinerant Kondo-lattice approach. Collective
spin exciton modes inside the hybridization gap around symmetry points of the
Brillouin zone may appear. This has been observed in heavy-fermion metal CeB6
and in particular in the Kondo insulators YbB12 and SmB6. The latter is also
the prime candidate for a strongly correlated topological insulator.
