The CDF and D0 experiments have collected large samples of b
hadrons during the 1992-1996 ppbar collider run at the Fermilab Tevatron.  We
report the discovery of the B_c meson in the semileptonic decay B_c -> j/psi l
nu X and give updates on B^0 - B-bar^0 mixing and B_s lifetime results.
Improved limits on the branching fractions of rare B decays are also shown.