  The dilatation operator measures scaling dimensions of local operator in a
conformal field theory. Algebraic methods of constructing the dilatation
operator in four-dimensional N=4 gauge theory are reviewed. These led to the
discovery of novel integrable spin chain models in the planar limit. Making use
of Bethe ansaetze, a superficial discrepancy in the AdS/CFT correspondence was
found, we discuss this issue and give a possible resolution.
