  We present an overview on extreme energy cosmic rays (EECR) and the
fundamental physics connected with them. The top-down and bottom-up scenarii
are contrasted. We summarize the essential features underlying the top-down
scenarii for EECR, namely, the lifetime and the mass {\bf imposed} to the heavy
relics whatever they be: topological and non-topological solitons, X-particles,
cosmic defects, microscopic black-holes, fundamental strings. An unified
formula for the quantum decay rate of all these objects was provided in
hep-ph/0202249. The key point in the top-down scenarii is the necessity to {\bf
adjust} the lifetime of the heavy object to the age of the universe. The
natural lifetimes of such heavy objects are, however, microscopic times
associated to the GUT energy scale (sim 10^{-28} sec. or shorter); such heavy
objects could have been abundantly formed by the end of inflation and it seems
natural they decayed shortly after being formed. The arguments produced to {\bf
fine tune} the relics lifetime to the age of the universe are critically
analyzed. The annihilation scenario (`Wimpzillas') is analyzed too. Top-down
scenarii based on networks of topological defects are strongly disfavored at
the light of the recent CMB anisotropy observations. We discuss the
acceleration mechanisms of cosmic rays,their possible astrophysical sources and
the main open physical problems and difficulties in the context of bottom-up
scenarii, and we conclude by outlining the expectations from future
observatories like EUSO and where the theoretical effort should be placed.
