  Any early universe phase transition occurring after inflation has the
potential to populate the universe with relic magnetic monopoles. Observations
of galactic magnetic fields, as well as observations matched with models for
extragalactic magnetic fields, lead to the conclusion that monopoles of mass
$\lsim 10^{15}$ GeV are accelerated in these fields to relativistic velocities.
We explore the possible signatures of a cosmic flux of relativistic monopoles
impinging on the earth. The electromagnetically-induced signatures of monopoles
are reliable. The hadronically-induced signatures are highly model-dependent.
Among our findings are (i) the electromagnetic energy losses of monopoles
continuously initiate a protracted shower of small intensity; (ii) monopoles
may traverse the earth's diameter, making them a probe of the earth's interior
structure; (iii) in addition to the direct monopole Cherenkov signal presently
employed, a very attractive search strategy for monopoles is detection of their
radio-Cherenkov signal produced by the coherent charge-excess in the $e^+-e^-$
shower - in fact, Cherenkov-detectors have the potential to discover a monopole
flux (or limit it) several orders of magnitude below the theoretical Parker
limit of $10^{-15}/\rm{cm}^2$/s/sr; (iv) it is conceivable (but not compelling)
that bound states of colored monopoles may be the primary particles initiating
the air showers observed above the GZK cutoff.
