Physics of extremely high-energy cosmic rays

Over the last third of the century, a few tens of events, detected by ground-based cosmic ray detectors, have opened a new window in the field of high-energy astrophysics. These events have macroscopic energies — exceeding 5×1019eV —, unobserved sources — if supposed to be in our vicinity —, an unknown chemical composition and a production and transport mechanism yet to be explained. With a flux as low as one particle per century per square kilometer, only dedicated detectors with huge apertures can bring in the high-quality and statistically significant data needed to answer those questions. In this article, we review the present status of the field both from an experimental and theoretical point of view. Special attention is given to the next generation of detectors devoted to the thorough exploration of the highest energy ranges.