The origin of the highest energy particles in the Universe is a mystery that persists despite experimental efforts that have intensified for 50 years. The issue has attracted keen theoretical interest in the last decade in response to evidence that the energy spectrum continues to energies above 10²⁰ eV without the cutoff expected from pion photoproduction. Explanations necessarily entail new fundamental physics or some unexpected astrophysics. Observations from different experiments are presently incommensurate, and more powerful observatories are under construction to discover and study the sources of the highest energy cosmic rays.

PACS numbers: 98.70.Sa, 98.70.Vc, 95.30.Cq