  In this review we discuss the important progress made in recent years towards
understanding the experimental data on cosmic rays with energies $\agt 10^{19}$
eV. We begin with a brief survey of the available data, including a description
of the energy spectrum, mass composition, and arrival directions. At this point
we also give a short overview of experimental techniques. After that, we
introduce the fundamentals of acceleration and propagation in order to discuss
the conjectured nearby cosmic ray sources. We then turn to theoretical notions
of physics beyond the Standard Model where we consider both exotic primaries
and exotic physical laws. Particular attention is given to the role that
TeV-scale gravity could play in addressing the origin of the highest energy
cosmic rays. In the final part of the review we discuss the potential of future
cosmic ray experiments for the discovery of tiny black holes that should be
produced in the Earth's atmosphere if TeV-scale gravity is realized in Nature.
