  The Odderon remains an elusive object, 33 years after its invention. The
Odderon is now a fundamental object in QCD and CGC and it has to be found
experimentally if QCD and CGC are right. In the present talk, we show how to
find it at RHIC and LHC. The most spectacular signature of the Odderon is the
predicted difference between the differential cross-sections for proton-proton
and antiproton-proton at high s and moderate t. This experiment can be done by
using the STAR detector at RHIC and by combining these future data with the
already present UA4/2 data. The Odderon could also be found by ATLAS experiment
at LHC by performing a high-precision measurement of the real part of the
hadron elastic scattering amplitude at small t.
