  It is not yet clear whether the observed flux suppression for ultra-high
energy cosmic rays (UHECR) at energies above \simeq 4.10E19 eV is a signature
of the Greisen-Zatsepin-Kuzmin (GZK) cutoff or corresponds, for instance, to
the maximum energies available at the relevant sources. Both phenomena can be
sensitive to violations of standard special relativity modifying cosmic-ray
propagation or acceleration at very high energy, and would in principle allow
to set bounds on Lorentz symmetry violation (LSV) parameters. But the precise
phenomenological analysis of the experimental data is far from trivial, and
other effects can be present. The effective parameters can be directly linked
to Planck-scale physics or to physics beyond Planck scale. If a vacuum rest
frame (VRF) exists, LSV can modify the internal structure of particles at very
high energy. Conventional symmetries may also cease to be valid at energies
close to the Planck scale. Other possible violations of fundamental principles
and conventional basic hypotheses (quantum mechanics, quark confinement, energy
and momentum conservation, vacuum homogeneity and "static" properties,
effective space dimensions...) can also be considered and possibly tested in
high-energy cosmic-ray experiments. Even below UHE (ultra-high energy), exotic
signatures cannot be excluded. We present an updated discussion of the
theoretical and phenomenological situation, including prospects for earth-based
and space experiments and a simple potential interpretation of the observed
UHECR composition in terms of LSV where the GZK cutoff would be replaced by
spontaneous emission of photons or e+ e- pairs. As the OPERA result on a
possible superluminal propagation of the muon neutrino was announced after the
conference, we briefly comment on the consistency problems that a \simeq 2.5 x
10E-5 critical speed anomaly for the muon neutrino can raise.
