  The e-e+ collider LEP, running at sqrt{s} = m(Z0), has been a copious source
of b-hadrons produced in decays Z0 -> b \b. We present recent studies using up
to 4*10^6 hadronic Z0 decays acquired by the DELPHI detector between 1992 and
2000. They rely on efficient particle identification, precise track and vertex
reconstruction and sophisticated data analysis algorithms.
  Presented are: a new measurement of the CKM matrix element |V_cb| in the
semileptonic exclusive decays B0_d -> D*+ l- \nu_l; a new measurement of the
B0_d - \B0_d oscillation frequency Delta(m_d); and searches by three methods
for B0_s - \B0_s oscillations, yielding new lower limits on Delta(m_s).
