Abstract　 　　
　The origin of the highest energy cosmic rays with energy >~ 10^{18} eV is a rather intricate puzzle, with a central question: how to accelerate particles to energies as high as 10^{20} eV or more, and in which astrophysical source? Other questions arise as well, such as: what are these cosmic rays, protons or nuclei? Why is there no powerful source in the arrival directions of the highest energy cosmic rays? This talk will summarize our current understanding in this field of research, and discuss various possible models of sources, with an emphasis put on acceleration physics.