  We discuss recent progress in multi-loop integrand reduction methods.
Motivated by the possibility of an automated construction of multi-loop
amplitudes via generalized unitarity cuts we describe a procedure to obtain a
general parameterisation of any multi-loop integrand in a renormalizable gauge
theory. The method relies on computational algebraic geometry techniques such
as Gr\"obner bases and primary decomposition of ideals. We present some results
for two and three loop amplitudes obtained with the help of the Macaulay2
computer algebra system and the Mathematica package BasisDet.
