It has not yet been elucidated whether the observed flux suppression for ultra-high energy cosmic rays (UHECR) at energies above ≃ 4 x 1019 eV is a signature of the Greisen-Zatsepin-Kuzmin (GZK) cutoff or a consequence of other phenomena. In both cases, violations of the standard fundamental principles of Physics can be present and play a significant role. They can in particular modify cosmic-ray interactions, propagation or acceleration at very high energy. Thus, in a long-term program, UHECR data can hopefully be used to test relativity, quantum mechanics, energy and momentum conservation, vacuum properties... as well as the elementariness of standard particles. Data on cosmic rays at energies ≃ 1020 eV may also be sensitive to new physic...