  We discuss QCD evolution equations for two and three particle correlation
functions of quarks and gluon fields in a hadron which describe development of
the momentum distribution of a parton system with a change of the wave length
of a probe which resolves it. We show in a general case of two-particle
correlators how the four-dimensional conformal algebra and the known pattern of
conformal symmetry breaking in QCD can be used to solve the complicated mixing
problem of local operators under renormalization and compute economically
anomalous dimensions of quark and gluon composite operators. An extension of
QCD to N = 1 super Yang-Mills theory and use of superconformal anomalies
arising after quantization allows to derive non-trivial relations between the
anomalous dimensions. For three-parton systems the conformal symmetry alone is
not enough to solve the three-particle problem. We show that in milticolor
limit of QCD there arises an extra conserved charge describing the solitonic
motion of the system of particles. The problem admits a one-to-one
correspondence with certain spin chain models which are exactly solvable.
