  Spin-selective insulators emerge in systems composed of fermions with two
internal degrees of freedom and another carrier, which could be fermionic or
bosonic. These insulators are characterized by a gapless state for one kind of
fermion and an insulator state for the other, with the latter satisfying a
commensurability relation that involves the other carrier. We review the
different scenarios where these unique insulators arise, focusing on Bose-Fermi
mixtures, the most recent and promising scenario for observing these insulators
in cold atom setups.
