  We review the theoretical approaches for investigations of the high energy
hadron-hadron scattering in the Regge kinematics. It is demonstrated, that the
gluon in QCD is reggeized and the Pomeron is a composite state of the reggeized
gluons. Remarkable properties of the BFKL equation for the Pomeron wave
function in QCD and supersymmetric gauge theories are outlined. Due to the
AdS/CFT correspondence the BFKL Pomeron is equivalent to the reggeized graviton
in the extended N=4 SUSY. The properties of the maximal transcendentality and
integrability are realized in this model. The BDS multi-gluon scattering
amplitudes are investigated in the Regge limit. They do not contain the
Mandelstam cuts and are not valid beyond one loop. It is shown, that the
hamiltonian for these composite states coincides with the hamiltonian of an
integrable open Heisenberg spin chain.
