  The Holstein Hubbard and Holstein t--J models are studied for a wide range of
phonon frequencies, electron--electron and electron--phonon interaction
strengths on finite lattices with up to ten sites by means of direct Lanczos
diagonalization. Previously the necessary truncation of the phononic Hilbert
space caused serious limitations to either very small systems (four or even two
sites) or to weak electron--phonon coupling, in particular in the adiabatic
regime. Using parallel computers we were able to investigate the transition
from `large' to `small' polarons in detail. By resolving the low--lying
eigenstates of the Hamiltonian and by calculating the spectral function we can
identify a polaron band in the strong--coupling case, whose dispersion deviates
from the free--particle dispersion at low and intermediate phonon frequencies.
For two electrons (holes) we establish the existence of bipolaronic states and
discuss the formation of a bipolaron band. For the 2D Holstein t--J model we
demonstrate that the formation of hole--polarons is favoured by strong Coulomb
correlations. Analyzing the hole--hole correlation functions we find that hole
binding is enhanced as a dynamical effect of the electron--phonon interaction.
