BFKL Equation: Status and Problems

The BFKL equation was derived for description of high energy behaviour of scattering amplitudes in non-Abelian gauge theories. Now it is widely known and used in quantum chromodynamics in the leading and next-to-leading logarithmic approximations. Its derivation is based on the pole Regge form of amplitudes with gluon exchanges in cross channels. In higher approximations this form is violated by contributions of Regge cuts, which complicates the derivation of the equation in the BFKL approach.