  The formation of a finite density multipolaronic state is analyzed in the
context of the Holstein model using the Dynamical Mean-Field Theory. The
spinless and spinful fermion cases are compared to disentangle the polaron
crossover from the bipolaron formation. The exact solution of Dynamical
Mean-Field Theory is compared with weak-coupling perturbation theory,
non-crossing (Migdal), and vertex correction approximations. We show that
polaron formation is not associated to a metal-insulator transition, which is
instead due to bipolaron formation.
