Recourse to recursion
relations: A primer on BCFW recursion and its generalisations

Scattering amplitudes are the crucial quantities connecting the theory of the Standard Model to the experimental outcomes as they are obtained at e.g. hadron colliders. Unfortunately, computing them using traditional Feynman diagram methods becomes prohibitively difficult as we analyse more complicated processes. In this review, we discuss one method developed to overcome this issue: the BCFW recursion relation, which decomposes scattering amplitudes into pairs of smaller on-shell amplitudes, connected by an on-shell particle carrying complex momentum. We review the spinor-helicity formalism and its use in the original proof of the BCFW recursion relation for tree-level Yang-Mills amplitudes. Following this, we discuss two generalisations of BCFW recursion: a translation to twistor space, and a recursion relation for
scalar effective field theories.