  The integrand-level methods for the reduction of scattering amplitudes are
well-established techniques, which have already proven their effectiveness in
several applications at one-loop. In addition to the automation and refinement
of tools for one-loop calculations, during the past year we observed very
interesting progress in developing new techniques for amplitudes at two- and
higher-loops, based on similar principles. In this presentation, we review the
main features of integrand-level approaches with a particular focus on
algebraic techniques, such as Laurent series expansion which we used to improve
the one-loop reduction, and multivariate polynomial division which unveils the
structure of multi-loop amplitudes.
