Abstract
This report is centred around tree-level scattering amplitudes in pure Yang–Mills theories, the most prominent example is given by the tree-level gluon amplitudes of QCD. I will discuss several ways of computing these amplitudes, illustrating in this way recent developments in perturbative quantum field theory. Topics covered in this review include colour decomposition, spinor and twistor methods, off- and on-shell recursion, MHV amplitudes and MHV expansion, the Grassmannian and the amplituhedron, the scattering equations and the CHY representation. At the end of this report there will be an outlook on the relation between pure Yang–Mills amplitudes and scattering amplitudes in perturbative quantum gravity.
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