  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.
