  We introduce a generic Froehlich-Coulomb model of the oxides, which also
includes infinite on-site (Hubbard) repulsion, and describe a simple analytical
method of solving the multi-polaron problem in complex lattice structures. Two
particular lattices, a zig-zag ladder and a perovskite layer, are studied. We
find that depending on the relative strength of the Froehlich and Coulomb
interactions these systems are either polaronic Fermi (or Luttinger)-liquids,
bipolaronic superconductors, or charge segregated insulators. In the
superconducting phase the carriers are superlight mobile bipolarons. The model
describes key features of the cuprates such as their Tc values, the isotope
effects, the normal state diamagnetism, pseudogap, and spectral functions
measured in tunnelling and photoemission. We argue that a low Fermi energy and
strong coupling of carriers with high-frequency phonons is the cause of high
critical temperatures in novel superconductors.
