I will review how generalized unitarity can be used (in principle) to determine (multi-)loop amplitudes. Although its application to compute one-loop amplitudes has been an incredible success, I will describe two important ways in which even this familiar story can be substantially improved: first, by introducing a new regularization scheme which renders all IR-safe observables manifestly dual-conformally invariant; and second, by upgrading the expansion into scalar boxes, triangles, and bubbles into a version which allows us to match field theory at the integrand level. This improved representation of one-loop amplitudes immediately suggests a strategy for going forward to higher loops. Indeed, applying these ideas to two-loop amplitudes in planar N=4 SYM will lead us to a closed-form local integrand-level representation of all two-loop scattering amplitudes.
