  We review efforts to unify both the Bardeen, Cooper and Schrieffer (BCS) and
Bose-Einstein condensation (BEC) pictures of superconductivity. We have finally
achieved this in terms of a "\textit{complete} boson-fermion (BF) model" (CBFM)
that reduces in special cases to all the main continuum (as opposed to "spin")
statistical theories of superconductivity. Our BF model is "complete" in the
sense that not only two-electron (2e) but also two-hole (2h) Cooper pairs (CPs)
are allowed in arbitrary proportions. In contrast, BCS-Bogoliubov theory--which
can also be considered as the theory of a mixture of kinematically independent
electrons, 2e- and 2h-CPs--allows only equal, 50%-50%, mixtures of the two
kinds of CPs. This is obvious from the perfect symmetry about $\mu$, the
electron chemical potential, of the well-known Bogoliubov $v^{2}(\epsilon)$ and
$u^{2}(\epsilon)$ coefficients, where $\epsilon$ is the electron energy. The
CBFM is then applied to see: a) whether the BCS model interaction for the
electron-phonon dynamical mechanism is sufficient to predict the unusually high
values of $T_{c}$ (in units of the Fermi temperature) of $\simeq 0.01-0.1$
exhibited by the so-called ``exotic'' superconductors \cite{Brandow} in both 2D
and 3D--relative to the low values of $\lesssim 10^{-3}$ more or less correctly
predicted by BCS theory for conventional, elemental superconductors; and b)
whether it can at least suggest, if not explain, why "hole superconductors"
have higher $T_{c}$'s.
