The hadronic contributions to the anomalous magnetic moment of the muon cannot be calculated perturbatively and is usually measured experimentally in ee→hadrons. This measurement is often carried out using radiative return where an extra hard photon is detected and thereby reducing the invariant mass of the hadrons. However, this increases the theoretical complexity of the event generators required to accurately model the process. An alternative but equally challenging method is the extraction in eμ→eμ through the MUonE experiment. Here, the signal is loop induced necessitating an understanding of the process to 10^-5.
To reach the required precision we require NNLO and even N^3LO predictions in QED. In this talk, I will discuss the methods required to reach this goal and include results for 2→2 processes at NNLO.