  We review recent progress in the understanding of symmetries for scattering
amplitudes in N=4 superconformal Yang-Mills theory. It is summarized how the
superficial breaking of superconformal symmetry by collinear anomalies and the
renormalization process can be cured at tree and loop level. This is achieved
by correcting the representation of the superconformal group on amplitudes.
Moreover, we comment on the Yangian symmetry of scattering amplitudes and how
it inherits these correction terms from the ordinary Lie algebra symmetry.
Invariants under this algebra and their relation to the Grassmannian generating
function for scattering amplitudes are discussed. Finally, parallel
developments in N=6 superconformal Chern-Simons theory are summarized. This
article is an invited review for a special issue of Journal of Physics A
devoted to Scattering Amplitudes in Gauge Theories.
