There is great interest in cosmic rays of energy above 10^19 eV, particularly as straightforward arguments suggest that there should be very few, if any, above 10^20 eV. I will review how such particles can be observed and overview the present situation with the data which leads to an enigma. To resolve this, a diverse range of proposals has been suggested, ranging from the hypothesis of new particles to the breakdown of Lorentz invariance. However, new data are badly needed and the Pierre Auger Observatory, in which there is significant UK involvement, is being constructed in Argentina to rectify the situation. I will describe the prospects for science from this instrument and show some early observations.