  The studies of a number of systems treated in terms of an inhomogeneous
(spatially separated) Fermi-Bose mixture with superconducting clusters or
droplets of the order parameter in a host medium with unpaired normal states
are reviewed. A spatially separated Fermi-Bose mixture is relevant to
superconducting BaKBiO3 bismuth oxides. Droplets of the order parameter can
occur in thin films of a dirty metal, described in the framework of the
strongly attractive two-dimensional Hubbard model at a low electron density
with a clearly pronounced diagonal disorder. The Bose-Einstein condensate
droplets are formed in mixtures and dipole gases with an imbalance in the
densities of the Fermi and Bose components. The Bose-Einstein condensate
clusters also arise at the center or at the periphery of a magnetic trap
involving spin-polarized Fermi gases. Exciton and plasmon collapsing droplets
can emerge in the presence of the exciton-exciton or plasmon-plasmon
interaction. The plasmon contribution to the charge screening in MgB2 leads to
the formation of spatially modulated inhomogeneous structures. In metallic
hydrogen and metal hydrides, droplets can be formed in shock-wave experiments
at the boundary of the first-order phase transition between the metallic and
molecular phases. In a spatially separated Fermi-Bose mixture arising in an
Aharonov-Bohm interference ring with a superconducting bridge in a
topologically nontrivial state, additional Fano resonances may appear and
collapse due to the presence of edge Majorana modes in the system.
