Exact superconformal and Yangian symmetry of scattering amplitudes

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 paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Scattering amplitudes in gauge theories'.