  In the framework of potential models for heavy quarkonium the mass spectrum
for the system ($\bar b c$) is considered. Spin-dependent splittings, taking
into account a change of a constant for effective coulomb interaction between
the quarks, and widths of radiative transitions between the ($\bar b c$) levels
are calculated. In the framework of QCD sum rules, masses of the lightest
vector $B_c^*$ and pseudoscalar $B_c$ states are estimated, scaling relation
for leptonic constants of heavy quarkonia is derived, and the leptonic constant
$f_{B_c}$ is evaluated. The $B_c$ decays are considered in the framework of
both the potential models and the QCD sum rules, where the significance of
Coulomb-like corrections is shown. The relations, following from the
approximate spin symmetry for the heavy quarks in the heavy quarkonium, are
analysed for the form factors of the semileptonic weak exclusive decays of
$B_c$. The $B_c$ lifetime is evaluated with the account of the corrections to
the spectator mechanism of the decay, because of the quark binding into the
meson. The total and differential cross sections of the $B_c$ production in
different interactions are calculated. The analytic expressions for the
fragmentational production cross sections of $B_c$ are derived. The possibility
of the practical $B_c$ search in the current and future experiments at
electron-positron and hadron colliders is analysed.
