  While several arguments can be proposed against the existence of particles
with energy in excess of $(3-5)\times 10^{19}$ eV in the cosmic ray spectrum,
these particles are actually observed and their origin seeks for an
explanation. After a description of the problems encountered in explaining
these ultra-high energy cosmic rays (UHECRs) in the context of astrophysical
sources, we will review the so-called {\it Top-Down} (TD) Models, in which
UHECRs are the result of the decay of very massive unstable particles, possibly
created in the Early Universe. Particular emphasis will be given to the
signatures of the TD models, likely to be accessible to upcoming experiments
like Auger.
