  We present a review of properties of ultracold atomic Fermi-Bose mixtures in
inhomogeneous and random optical lattices. In the strong interacting limit and
at very low temperatures, fermions form, together with bosons or bosonic holes,
{\it composite fermions}. Composite fermions behave as a spinless interacting
Fermi gas, and in the presence of local disorder they interact via random
couplings and feel effective random local potential. This opens a wide variety
of possibilities of realizing various kinds of ultracold quantum disordered
systems. In this paper we review these possibilities, discuss the accessible
quantum disordered phases, and methods for their detection. The discussed
quantum phases include Fermi glasses, quantum spin glasses, "dirty"
superfluids, disordered metallic phases, and phases involving quantum
percolation.
