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In this talk, I will discuss recent calculations of amplitudes for $\gamma^\ast$, $\gamma\gamma$, $\gamma\gamma j$, and off-shell Drell-Yan production. Results include, in particular, the first complete QCD amplitudes for four-point scattering at three loops and five-point scattering at two loops. New techniques for finite field reduction, analytical integration of Feynman integrals and multivariate partial fraction decomposition enabled these calculations and will be discussed in some detail.