  We develop a semi-quantitative theory of electron pairing and resulting
superconductivity in bulk "poor conductors" in which Fermi energy $E_F$ is
located in the region of localized states not so far from the Anderson mobility
edge $E_c$. We review the existing theories and experimental data and argue
that a large class of disordered films is described by this model.
  Our theoretical analysis is based on the analytical treatment of pairing
correlations, described in the basis of the exact single-particle eigenstates
of the 3D Anderson model, which we combine with numerical data on eigenfunction
correlations. Fractal nature of critical wavefunction's correlations is shown
to be crucial for the physics of these systems.
  We identify three distinct phases: 'critical' superconductive state formed at
$E_F=E_c$, superconducting state with a strong pseudogap, realized due to
pairing of weakly localized electrons and insulating state realized at $E_F$
still deeper inside localized band. The 'critical' superconducting phase is
characterized by the enhancement of the transition temperature with respect to
BCS result, by the inhomogeneous spatial distribution of superconductive order
parameter and local density of states. The major new feature of the
pseudo-gaped state is the presence of two independent energy scales:
superconducting gap $\Delta$, that is due to many-body correlations and a new
"pseudogap" energy scale $\Delta_P$ which characterizes typical binding energy
of localized electron pairs and leads to the insulating behavior of the
resistivity as a function of temperature above superconductive $T_c$. Two gap
nature of the "pseudo-gaped superconductor" is shown to lead to a number of
unusual physical properties.
