  In recent years, the BCFW construction provided a very powerful tool for
computing scattering amplitudes as well as it shed light on the perturbation
theory structure. In this talk, we discuss the long-standing issue of the
boundary term arising when the amplitudes do not vanish as some momenta are
taken to infinity along some complex direction. In particular, we provide a new
set of on-shell recursion relations valid for such theories and discuss its
consequences on our understanding on the perturbation theory structure of the
S-Matrix.
