  The mean-field theory represents a useful starting point for studying
carrier-induced ferromagnetism in Mn$_x$III$_{1-x}$V diluted magnetic
semiconductors. A detail description of these systems requires to include
correlations in the many-body hole system. We discuss the effects of
correlations among itinerant carriers on magnetic properties of bulk
Mn$_x$III$_{1-x}$V and magnetic semiconductor quantum wells. Presented results
were obtained using parabolic band approximation and we also derive a many-body
perturbation technique that allows to account for hole-hole correlations in
realistic semiconductor valence bands.
