  The single bipolaron problem is examined in the context of the 1D
Holstein-Hubbard model, emphasizing analogies and differences with respect to
the complementary single polaron physics. The bipolaron band structure below
the phonon threshold is revealed, showing a complex relationship between
numerous excited bands as the adiabatic limit is approached. Light bipolarons
with significant binding energy, the stability of large bipolarons, the small
to large bipolaron crossover as a function of the Hubbard repulsion, as well as
the bipolaron dissociation, are investigated in detail, disentangling
adiabatic, nonadiabatic and lattice coarsening effects. It is emphasized that
condensation of bipolarons occurs in the dilute limit only at very low
temperatures.
