  We shortly discuss several astrophysical scenarios leading to cosmic ray
acceleration up to extremely high energies reaching the scale of 10^{20} eV.
The processes suggested in the literature include acceleration at relativistic
jet terminal shocks and shear boundary layers, shocks in large scale accretion
flows onto supergalactic cosmic structures, particle reflections from
ultra-relativistic shocks postulated to exist in sources of gamma ray bursts,
the processes involving the neutron star rotating magnetospheres and dormant
quasars. Some of these objects can explain cosmic rays with highest energies if
one tunes the model parameters to limits enabling the highest acceleration
efficiency. We also note that some of the considered processes allow for
acceleration efficiency in the Hillas diagram, beta, to be much larger than
unity. The present paper is based on a review talk presented during the
European Cosmic Ray Symposium in Lodz (2000).
