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New structures in scattering amplitudes: a review

We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering amplitudes in general interacting theories. We describe their tree-level structure and their on-shell representations, as well as the links between the tree-level structure itself and the structure of the loop amplitudes. Finally, we describe the on-shell diagrammatics recently proposed both on general grounds and in the remarkable example of planar supersymmetric theories. This review is partially based on lectures given at: Dipartimento di Fisica and INFN, Università di Bologna; Departamento de Fısica de Partıculas, Universidade de Santiago de Compostela; and as part of the program Strings@ar Lectures on Advanced Topics of High Energy Physics held at the IAFE