  We study the properties of color-singlet Reggeon compound states in
multicolor high-energy QCD in four dimensions. Their spectrum is governed by
completely integrable (1+1)-dimensional effective QCD Hamiltonian whose
diagonalization within the Bethe Ansatz leads to the Baxter equation for the
Heisenberg spin magnet. We show that nonlinear WKB solution of the Baxter
equation gives rise to the same integrable structures as appeared in the
Seiberg-Witten solution for $N=2$ SUSY QCD and in the finite-gap solutions of
the soliton equations. We explain the origin of hyperelliptic Riemann surfaces
out of QCD in the Regge limit and discuss the meaning of the Whitham dynamics
on the moduli space of quantum numbers of the Reggeon compound states, QCD
Pomerons and Odderons.
